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<XMTok font="italic" role="UNKNOWN">b</XMTok>
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<XMath>
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<XMApp>
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<XMWrap>
<XMApp xml:id="S0.Ex9.m1.3">
<XMTok name="varobar" role="RELOP">⦶</XMTok>
<XMDual>
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<XMRef idref="S0.Ex9.m1.1"/>
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<XMApp xml:id="S0.Ex9.m1.3.1">
<XMTok name="varoast" role="MULOP">⊛</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex9.m1.4">
<XMTok name="varogreaterthan" role="RELOP">⧁</XMTok>
<XMDual>
<XMApp>
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<XMRef idref="S0.Ex9.m1.2"/>
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<XMWrap>
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<XMTok name="varobslash" role="MULOP">⦸</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex9.m1.4.2">
<XMTok name="varocircle" role="MULOP">⊚</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex9.m1.4.3">
<XMTok name="varodot" role="MULOP">⊙</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok font="italic" role="UNKNOWN" xml:id="S0.Ex9.m1.2">a</XMTok>
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<XMTok font="italic" role="UNKNOWN">b</XMTok>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex9.m1.5">
<XMTok name="varolessthan" role="RELOP">⧀</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
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</XMath>
</Math>
</equation>
<equation xml:id="S0.Ex10">
<Math mode="display" tex="a\varominus b\quad a\varoplus b\quad a\varoslash b\quad a\varotimes b\quad a% \varovee b\quad a\varowedge b\quad a\vartimes b" text="formulae@(list@(a varominus b, a additive-disjunction b, a) varoslash b, list@(a multiplicative-conjunction b, a) varovee b, a varowedge list@(b, a vartimes b))" xml:id="S0.Ex10.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex10.m1.4"/>
<XMRef idref="S0.Ex10.m1.5"/>
<XMRef idref="S0.Ex10.m1.6"/>
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<XMWrap>
<XMApp xml:id="S0.Ex10.m1.4">
<XMTok name="varoslash" role="RELOP">⊘</XMTok>
<XMDual>
<XMApp>
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<XMWrap>
<XMApp xml:id="S0.Ex10.m1.4.1">
<XMTok name="varominus" role="ADDOP">⊖</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex10.m1.4.2">
<XMTok meaning="additive-disjunction" name="varoplus" role="ADDOP">⊕</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok font="italic" role="UNKNOWN" xml:id="S0.Ex10.m1.1">a</XMTok>
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</XMDual>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex10.m1.5">
<XMTok name="varovee" role="RELOP">∨⃝</XMTok>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S0.Ex10.m1.5.1"/>
<XMRef idref="S0.Ex10.m1.2"/>
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<XMWrap>
<XMApp xml:id="S0.Ex10.m1.5.1">
<XMTok meaning="multiplicative-conjunction" name="varotimes" role="MULOP">⊗</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok font="italic" role="UNKNOWN" xml:id="S0.Ex10.m1.2">a</XMTok>
</XMWrap>
</XMDual>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex10.m1.6">
<XMTok name="varowedge" role="RELOP">∧⃝</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S0.Ex10.m1.3"/>
<XMRef idref="S0.Ex10.m1.6.1"/>
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<XMWrap>
<XMTok font="italic" role="UNKNOWN" xml:id="S0.Ex10.m1.3">b</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex10.m1.6.1">
<XMTok name="vartimes" role="MULOP">×</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMApp>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S0.Ex11">
<Math mode="display" tex="\bigbox\quad\bigcurlywedge\quad\bigcurlyvee\quad\biginterleave\quad\bignplus% \quad\bigparallel\quad\bigsqcap\quad\bigtriangledown\quad\bigtriangleup" text="list@(bigbox, bigcurlywedge, bigcurlyvee, biginterleave, intersection-plus, bigparallel, bigsqcap, bigtriangledown, bigtriangleup)" xml:id="S0.Ex11.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S0.Ex11.m1.1"/>
<XMRef idref="S0.Ex11.m1.2"/>
<XMRef idref="S0.Ex11.m1.3"/>
<XMRef idref="S0.Ex11.m1.4"/>
<XMRef idref="S0.Ex11.m1.5"/>
<XMRef idref="S0.Ex11.m1.6"/>
<XMRef idref="S0.Ex11.m1.7"/>
<XMRef idref="S0.Ex11.m1.8"/>
<XMRef idref="S0.Ex11.m1.9"/>
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<XMWrap>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok fontsize="160%" mathstyle="display" name="bigcurlywedge" role="SUMOP" scriptpos="mid" xml:id="S0.Ex11.m1.2">⋏</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok fontsize="160%" mathstyle="display" name="bigcurlyvee" role="SUMOP" scriptpos="mid" xml:id="S0.Ex11.m1.3">⋎</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok mathstyle="display" name="biginterleave" role="SUMOP" scriptpos="mid" xml:id="S0.Ex11.m1.4">⫼</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual role="ADDOP" xml:id="S0.Ex11.m1.5">
<XMTok mathstyle="display" meaning="intersection-plus" name="bignplus" role="ADDOP"/>
<XMWrap rule="kludge">
<XMTok mathstyle="display" meaning="intersection" name="bigcap" role="SUMOP" scriptpos="mid">⋂</XMTok>
<XMTok meaning="plus" role="ADDOP" width="0pt" xoffset="-1.6em" yoffset="0.2ex">+</XMTok>
</XMWrap>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok mathstyle="display" name="bigparallel" role="SUMOP" scriptpos="mid" xml:id="S0.Ex11.m1.6">‖</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok mathstyle="display" name="bigsqcap" role="SUMOP" scriptpos="mid" xml:id="S0.Ex11.m1.7">⨅</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok fontsize="160%" mathstyle="display" name="bigtriangledown" role="SUMOP" scriptpos="mid" xml:id="S0.Ex11.m1.8">▽</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok fontsize="160%" mathstyle="display" name="bigtriangleup" role="SUMOP" scriptpos="mid" xml:id="S0.Ex11.m1.9">△</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
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<para xml:id="p2">
<equation xml:id="S0.Ex12">
<Math mode="display" tex="\textstyle\bigbox\quad\bigcurlywedge\quad\bigcurlyvee\quad\biginterleave\quad% \bignplus\quad\bigparallel\quad\bigsqcap\quad\bigtriangledown\quad\bigtriangleup" text="list@(bigbox, bigcurlywedge, bigcurlyvee, biginterleave, intersection-plus, bigparallel, bigsqcap, bigtriangledown, bigtriangleup)" xml:id="S0.Ex12.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S0.Ex12.m1.1"/>
<XMRef idref="S0.Ex12.m1.2"/>
<XMRef idref="S0.Ex12.m1.3"/>
<XMRef idref="S0.Ex12.m1.4"/>
<XMRef idref="S0.Ex12.m1.5"/>
<XMRef idref="S0.Ex12.m1.6"/>
<XMRef idref="S0.Ex12.m1.7"/>
<XMRef idref="S0.Ex12.m1.8"/>
<XMRef idref="S0.Ex12.m1.9"/>
</XMApp>
<XMWrap>
<XMTok fontsize="160%" mathstyle="text" name="bigbox" role="SUMOP" scriptpos="post" xml:id="S0.Ex12.m1.1">□</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok fontsize="160%" mathstyle="text" name="bigcurlywedge" role="SUMOP" scriptpos="post" xml:id="S0.Ex12.m1.2">⋏</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok fontsize="160%" mathstyle="text" name="bigcurlyvee" role="SUMOP" scriptpos="post" xml:id="S0.Ex12.m1.3">⋎</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok mathstyle="text" name="biginterleave" role="SUMOP" scriptpos="post" xml:id="S0.Ex12.m1.4">⫼</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual role="ADDOP" xml:id="S0.Ex12.m1.5">
<XMTok mathstyle="text" meaning="intersection-plus" name="bignplus" role="ADDOP"/>
<XMWrap rule="kludge">
<XMTok mathstyle="text" meaning="intersection" name="bigcap" role="SUMOP" scriptpos="post">⋂</XMTok>
<XMTok meaning="plus" role="ADDOP" width="0pt" xoffset="-1.3em" yoffset="0.2ex">+</XMTok>
</XMWrap>
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<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok mathstyle="text" name="bigparallel" role="SUMOP" scriptpos="post" xml:id="S0.Ex12.m1.6">‖</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok mathstyle="text" name="bigsqcap" role="SUMOP" scriptpos="post" xml:id="S0.Ex12.m1.7">⨅</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok fontsize="160%" mathstyle="text" name="bigtriangledown" role="SUMOP" scriptpos="post" xml:id="S0.Ex12.m1.8">▽</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok fontsize="160%" mathstyle="text" name="bigtriangleup" role="SUMOP" scriptpos="post" xml:id="S0.Ex12.m1.9">△</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
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<para xml:id="p3">
<equation xml:id="S0.Ex13">
<Math mode="display" tex="{\displaystyle\bignplus}\qquad{\textstyle\bignplus}\qquad{\scriptstyle% \bignplus}\qquad{\scriptscriptstyle\bignplus}" text="list@(intersection-plus, intersection-plus, intersection-plus, intersection-plus)" xml:id="S0.Ex13.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S0.Ex13.m1.1"/>
<XMRef idref="S0.Ex13.m1.2"/>
<XMRef idref="S0.Ex13.m1.3"/>
<XMRef idref="S0.Ex13.m1.4"/>
</XMApp>
<XMWrap>
<XMDual role="ADDOP" xml:id="S0.Ex13.m1.1">
<XMTok mathstyle="display" meaning="intersection-plus" name="bignplus" role="ADDOP"/>
<XMWrap rule="kludge">
<XMTok mathstyle="display" meaning="intersection" name="bigcap" role="SUMOP" scriptpos="mid">⋂</XMTok>
<XMTok meaning="plus" role="ADDOP" width="0pt" xoffset="-1.6em" yoffset="0.2ex">+</XMTok>
</XMWrap>
</XMDual>
<XMHint name="qquad" role="PUNCT" width="20pt"/>
<XMDual role="ADDOP" xml:id="S0.Ex13.m1.2">
<XMTok mathstyle="text" meaning="intersection-plus" name="bignplus" role="ADDOP"/>
<XMWrap rule="kludge">
<XMTok mathstyle="text" meaning="intersection" name="bigcap" role="SUMOP" scriptpos="post">⋂</XMTok>
<XMTok meaning="plus" role="ADDOP" width="0pt" xoffset="-1.3em" yoffset="0.2ex">+</XMTok>
</XMWrap>
</XMDual>
<XMHint name="qquad" role="PUNCT" width="20pt"/>
<XMDual role="ADDOP" xml:id="S0.Ex13.m1.3">
<XMTok mathstyle="text" meaning="intersection-plus" name="bignplus" role="ADDOP"/>
<XMWrap rule="kludge">
<XMTok fontsize="70%" mathstyle="text" meaning="intersection" name="bigcap" role="SUMOP" scriptpos="post">⋂</XMTok>
<XMTok fontsize="70%" meaning="plus" role="ADDOP" width="0pt" xoffset="-1.3em" yoffset="0.2ex">+</XMTok>
</XMWrap>
</XMDual>
<XMHint name="qquad" role="PUNCT" width="20pt"/>
<XMDual role="ADDOP" xml:id="S0.Ex13.m1.4">
<XMTok mathstyle="text" meaning="intersection-plus" name="bignplus" role="ADDOP"/>
<XMWrap rule="kludge">
<XMTok fontsize="50%" mathstyle="text" meaning="intersection" name="bigcap" role="SUMOP" scriptpos="post">⋂</XMTok>
<XMTok fontsize="50%" meaning="plus" role="ADDOP" width="0pt" xoffset="-1.3em" yoffset="0.2ex">+</XMTok>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
<para xml:id="p4">
<equation xml:id="S0.Ex14">
<Math mode="display" tex="\inplus\quad\niplus\quad\ntrianglelefteqslant\quad\ntrianglerighteqslant\quad% \trianglelefteqslant\quad\trianglerighteqslant" text="list@(inplus, niplus, ntrianglelefteqslant, ntrianglerighteqslant, trianglelefteqslant, trianglerighteqslant)" xml:id="S0.Ex14.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S0.Ex14.m1.1"/>
<XMRef idref="S0.Ex14.m1.2"/>
<XMRef idref="S0.Ex14.m1.3"/>
<XMRef idref="S0.Ex14.m1.4"/>
<XMRef idref="S0.Ex14.m1.5"/>
<XMRef idref="S0.Ex14.m1.6"/>
</XMApp>
<XMWrap>
<XMTok name="inplus" role="RELOP" xml:id="S0.Ex14.m1.1">⨭</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok name="niplus" role="RELOP" xml:id="S0.Ex14.m1.2">⨮</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok name="ntrianglelefteqslant" role="RELOP" xml:id="S0.Ex14.m1.3">⋬</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok name="ntrianglerighteqslant" role="RELOP" xml:id="S0.Ex14.m1.4">⋭</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok name="trianglelefteqslant" role="RELOP" xml:id="S0.Ex14.m1.5">⊴</XMTok>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMTok name="trianglerighteqslant" role="RELOP" xml:id="S0.Ex14.m1.6">⊵</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S0.Ex15">
<Math mode="display" tex="a\subsetplus b\quad a\subsetpluseq b\quad a\supsetplus b\quad a\supsetpluseq b" text="formulae@(a subset-plus b, formulae@(a subset-equals-plus b, formulae@(a superset-plus b, a superset-equals-plus b)))" xml:id="S0.Ex15.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex15.m1.1"/>
<XMRef idref="S0.Ex15.m1.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex15.m1.1">
<XMDual role="RELOP">
<XMTok meaning="subset-plus" name="subsetplus" role="RELOP"/>
<XMWrap rule="kludge">
<XMTok meaning="subset-of" name="subset" role="RELOP">⊂</XMTok>
<XMTok fontsize="50%" meaning="plus" role="ADDOP" width="0pt" xoffset="-0.8em" yoffset="0.3ex">+</XMTok>
</XMWrap>
</XMDual>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex15.m1.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex15.m1.2.1"/>
<XMRef idref="S0.Ex15.m1.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex15.m1.2.1">
<XMDual role="RELOP">
<XMTok meaning="subset-equals-plus" name="subsetpluseq" role="RELOP"/>
<XMWrap rule="kludge">
<XMTok meaning="subset-of-or-equals" name="subseteq" role="RELOP">⊆</XMTok>
<XMTok fontsize="50%" meaning="plus" role="ADDOP" width="0pt" xoffset="-0.8em" yoffset="0.5ex">+</XMTok>
</XMWrap>
</XMDual>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex15.m1.2.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex15.m1.2.2.1"/>
<XMRef idref="S0.Ex15.m1.2.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex15.m1.2.2.1">
<XMDual role="RELOP">
<XMTok meaning="superset-plus" name="supsetplus" role="RELOP"/>
<XMWrap rule="kludge">
<XMTok meaning="superset-of" name="supset" role="RELOP">⊃</XMTok>
<XMTok fontsize="50%" meaning="plus" role="ADDOP" width="0pt" xoffset="-1em" yoffset="0.3ex">+</XMTok>
</XMWrap>
</XMDual>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex15.m1.2.2.2">
<XMDual role="RELOP">
<XMTok meaning="superset-equals-plus" name="supsetpluseq" role="RELOP"/>
<XMWrap rule="kludge">
<XMTok meaning="superset-of-or-equals" name="supseteq" role="RELOP">⊇</XMTok>
<XMTok fontsize="50%" meaning="plus" role="ADDOP" width="0pt" xoffset="-1em" yoffset="0.5ex">+</XMTok>
</XMWrap>
</XMDual>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S0.Ex16">
<Math mode="display" tex="a\mapsfromchar b\quad a\mapsfrom b\quad a\Mapsfromchar b\quad a\Mapsfrom b% \quad a\longmapsfrom b\quad a\Longmapsfrom b\quad" text="formulae@(a mapsfromchar b, formulae@(a mapsfrom b, formulae@(a Mapsfromchar b, formulae@(a Mapsfrom b, formulae@(a longmapsfrom b, a Longmapsfrom b)))))" xml:id="S0.Ex16.m1">
<XMath>
<XMDual>
<XMRef idref="S0.Ex16.m1.1"/>
<XMWrap>
<XMDual xml:id="S0.Ex16.m1.1">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex16.m1.1.1"/>
<XMRef idref="S0.Ex16.m1.1.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex16.m1.1.1">
<XMTok name="mapsfromchar" role="RELOP">|</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex16.m1.1.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex16.m1.1.2.1"/>
<XMRef idref="S0.Ex16.m1.1.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex16.m1.1.2.1">
<XMTok name="mapsfrom" role="ARROW">↤</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex16.m1.1.2.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex16.m1.1.2.2.1"/>
<XMRef idref="S0.Ex16.m1.1.2.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex16.m1.1.2.2.1">
<XMTok name="Mapsfromchar" role="RELOP">|</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex16.m1.1.2.2.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex16.m1.1.2.2.2.1"/>
<XMRef idref="S0.Ex16.m1.1.2.2.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex16.m1.1.2.2.2.1">
<XMTok name="Mapsfrom" role="ARROW">⤆</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex16.m1.1.2.2.2.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex16.m1.1.2.2.2.2.1"/>
<XMRef idref="S0.Ex16.m1.1.2.2.2.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex16.m1.1.2.2.2.2.1">
<XMTok name="longmapsfrom" role="ARROW">⟻</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex16.m1.1.2.2.2.2.2">
<XMTok name="Longmapsfrom" role="ARROW">⟽</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
<XMHint name="quad" role="PUNCT" width="10pt"/>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S0.Ex17">
<Math mode="display" tex="a\Mapstochar b\quad a\Mapsto b\quad a\Longmapsto b\quad" text="formulae@(a Mapstochar b, formulae@(a Mapsto b, a Longmapsto b))" xml:id="S0.Ex17.m1">
<XMath>
<XMDual>
<XMRef idref="S0.Ex17.m1.1"/>
<XMWrap>
<XMDual xml:id="S0.Ex17.m1.1">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex17.m1.1.1"/>
<XMRef idref="S0.Ex17.m1.1.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex17.m1.1.1">
<XMTok name="Mapstochar" role="RELOP">|</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex17.m1.1.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex17.m1.1.2.1"/>
<XMRef idref="S0.Ex17.m1.1.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex17.m1.1.2.1">
<XMTok name="Mapsto" role="ARROW">⤇</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex17.m1.1.2.2">
<XMTok name="Longmapsto" role="ARROW">⟾</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
<XMHint name="quad" role="PUNCT" width="10pt"/>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
<para xml:id="p5">
<equation xml:id="S0.Ex18">
<Math mode="display" tex="a\nnearrow b\quad a\nnwarrow b\quad a\ssearrow b\quad a\sswarrow b" text="formulae@(a nnearrow b, formulae@(a nnwarrow b, formulae@(a ssearrow b, a sswarrow b)))" xml:id="S0.Ex18.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex18.m1.1"/>
<XMRef idref="S0.Ex18.m1.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex18.m1.1">
<XMTok class="ltx_nounicode" name="nnearrow" role="ARROW">\nnearrow</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex18.m1.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex18.m1.2.1"/>
<XMRef idref="S0.Ex18.m1.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex18.m1.2.1">
<XMTok class="ltx_nounicode" name="nnwarrow" role="ARROW">\nnwarrow</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex18.m1.2.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex18.m1.2.2.1"/>
<XMRef idref="S0.Ex18.m1.2.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex18.m1.2.2.1">
<XMTok class="ltx_nounicode" name="ssearrow" role="ARROW">\ssearrow</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex18.m1.2.2.2">
<XMTok class="ltx_nounicode" name="sswarrow" role="ARROW">\sswarrow</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
<para xml:id="p6">
<equation xml:id="S0.Ex19">
<Math mode="display" tex="a\leftarrowtriangle b\quad a\rightarrowtriangle b\quad a% \leftrightarrowtriangle b\quad a\leftrightarroweq b\quad a\lightning b" text="formulae@(a leftarrowtriangle b, formulae@(a rightarrowtriangle b, formulae@(a leftrightarrowtriangle b, formulae@(a leftrightarroweq b, a lightning b))))" xml:id="S0.Ex19.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex19.m1.1"/>
<XMRef idref="S0.Ex19.m1.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex19.m1.1">
<XMTok name="leftarrowtriangle" role="ARROW">⇽</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex19.m1.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex19.m1.2.1"/>
<XMRef idref="S0.Ex19.m1.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex19.m1.2.1">
<XMTok name="rightarrowtriangle" role="ARROW">⇾</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex19.m1.2.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex19.m1.2.2.1"/>
<XMRef idref="S0.Ex19.m1.2.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex19.m1.2.2.1">
<XMTok name="leftrightarrowtriangle" role="ARROW">⇿</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex19.m1.2.2.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex19.m1.2.2.2.1"/>
<XMRef idref="S0.Ex19.m1.2.2.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex19.m1.2.2.2.1">
<XMDual role="ARROW">
<XMTok name="leftrightarroweq" role="ARROW"/>
<XMApp role="RELOP">
<XMTok role="SUPERSCRIPTOP" scriptpos="mid1"/>
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMTok fontsize="70%" name="leftrightarrow" role="METARELOP">↔</XMTok>
</XMApp>
</XMDual>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex19.m1.2.2.2.2">
<XMTok name="lightning" role="ARROW">↯</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
<para xml:id="p7">
<equation xml:id="S0.Ex20">
<Math mode="display" tex="a\shortdownarrow b\quad a\shortleftarrow b\quad a\shortrightarrow b\quad a\shortuparrow b" text="formulae@(a shortdownarrow b, formulae@(a shortleftarrow b, formulae@(a shortrightarrow b, a shortuparrow b)))" xml:id="S0.Ex20.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex20.m1.1"/>
<XMRef idref="S0.Ex20.m1.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex20.m1.1">
<XMTok name="shortdownarrow" role="ARROW">↓</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex20.m1.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex20.m1.2.1"/>
<XMRef idref="S0.Ex20.m1.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex20.m1.2.1">
<XMTok name="shortleftarrow" role="ARROW">←</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex20.m1.2.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex20.m1.2.2.1"/>
<XMRef idref="S0.Ex20.m1.2.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex20.m1.2.2.1">
<XMTok name="shortrightarrow" role="ARROW">→</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex20.m1.2.2.2">
<XMTok name="shortuparrow" role="ARROW">↑</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S0.Ex21">
<Math mode="display" tex="a\arrownot b\quad a\longarrownot b\quad a\Arrownot b\quad a\Longarrownot b" text="formulae@(a arrownot b, formulae@(a longarrownot b, formulae@(a Arrownot b, a Longarrownot b)))" xml:id="S0.Ex21.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex21.m1.1"/>
<XMRef idref="S0.Ex21.m1.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex21.m1.1">
<XMTok meaning="divide" name="arrownot" role="RELOP" width="0pt">/</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex21.m1.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex21.m1.2.1"/>
<XMRef idref="S0.Ex21.m1.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex21.m1.2.1">
<XMTok meaning="divide" name="longarrownot" role="RELOP" width="0pt">/</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMDual xml:id="S0.Ex21.m1.2.2">
<XMApp>
<XMTok meaning="formulae"/>
<XMRef idref="S0.Ex21.m1.2.2.1"/>
<XMRef idref="S0.Ex21.m1.2.2.2"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex21.m1.2.2.1">
<XMTok meaning="divide" name="Arrownot" role="RELOP" width="0pt">/</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMApp xml:id="S0.Ex21.m1.2.2.2">
<XMTok meaning="divide" name="Longarrownot" role="RELOP" width="0pt">/</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
<para xml:id="p8">
<equation xml:id="S0.Ex22">
<Math class="ltx_math_unparsed" mode="display" tex="\Lbag 42\Rbag\quad\lbag 42\rbag\quad" xml:id="S0.Ex22.m1">
<XMath>
<XMWrap>
<XMTok name="Lbag" role="OPEN">⟅</XMTok>
<XMTok meaning="42" role="NUMBER" xml:id="S0.Ex22.m1.1">42</XMTok>
<XMTok name="Rbag" role="CLOSE">⟆</XMTok>
</XMWrap>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMWrap>
<XMTok name="lbag" role="OPEN">⟅</XMTok>
<XMTok meaning="42" role="NUMBER">42</XMTok>
<XMTok name="rbag" role="CLOSE">⟆</XMTok>
</XMWrap>
<XMHint name="quad" role="PUNCT" width="10pt"/>
</XMath>
</Math>
</equation>
<equation xml:id="S0.Ex23">
<Math class="ltx_math_unparsed" mode="display" tex="\llbracket 42\rrbracket\quad\llfloor 42\rrfloor\quad\llceil 42\rrceil\quad% \llparenthesis 42\rrparenthesis" xml:id="S0.Ex23.m1">
<XMath>
<XMWrap>
<XMTok name="llbracket" role="OPEN">⟦</XMTok>
<XMTok meaning="42" role="NUMBER" xml:id="S0.Ex23.m1.1">42</XMTok>
<XMTok name="rrbracket" role="CLOSE">⟧</XMTok>
</XMWrap>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMWrap>
<XMDual role="OPEN">
<XMTok name="llfloor" role="OPEN"/>
<XMWrap rule="kludge">
<XMTok name="lfloor" role="OPEN" stretchy="false" width="0pt" xoffset="0.3em">⌊</XMTok>
<XMTok name="lfloor" role="OPEN" stretchy="false">⌊</XMTok>
</XMWrap>
</XMDual>
<XMTok meaning="42" role="NUMBER">42</XMTok>
<XMDual role="CLOSE">
<XMTok name="rrfloor" role="CLOSE"/>
<XMWrap rule="kludge">
<XMTok name="rfloor" role="CLOSE" stretchy="false">⌋</XMTok>
<XMTok name="rfloor" role="CLOSE" stretchy="false" width="0pt" xoffset="-0.31em">⌋</XMTok>
</XMWrap>
</XMDual>
</XMWrap>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMWrap>
<XMDual role="OPEN">
<XMTok name="llceil" role="OPEN"/>
<XMWrap rule="kludge">
<XMTok name="lceil" role="OPEN" stretchy="false" width="0pt" xoffset="0.3em">⌈</XMTok>
<XMTok name="lceil" role="OPEN" stretchy="false">⌈</XMTok>
</XMWrap>
</XMDual>
<XMTok meaning="42" role="NUMBER">42</XMTok>
<XMDual role="CLOSE">
<XMTok name="rrceil" role="CLOSE"/>
<XMWrap rule="kludge">
<XMTok name="rceil" role="CLOSE" stretchy="false">⌉</XMTok>
<XMTok name="rceil" role="CLOSE" stretchy="false" width="0pt" xoffset="-0.3em">⌉</XMTok>
</XMWrap>
</XMDual>
</XMWrap>
<XMHint name="quad" role="PUNCT" width="10pt"/>
<XMWrap>
<XMTok name="llparenthesis" role="OPEN">⦇</XMTok>
<XMTok meaning="42" role="NUMBER">42</XMTok>
<XMTok name="rrparenthesis" role="CLOSE">⦈</XMTok>
</XMWrap>
</XMath>
</Math>
</equation>
<p>©</p>
</para>
</document>