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File:StrictContent/ArithmeticAlgebraLogic/logic6
CVS-ID:
Author:Design Science, Inc. (E. Cannon, E. Tabacman, R.Miner)
Description:not (forall s in S where f(s) is in T) = (there exists s in S such that f(s) is not in T)

Sample Rendering:

$\mathrm{eq}(\mathrm{not}(\mathrm{forall}s\mathrm{implies}(\mathrm{in}(s, \mathrm{suchthat}(R, \mathrm{lambda}s\mathrm{in}(s, S))), \mathrm{in}(f(x), T))), \mathrm{exists}s\mathrm{and}(\mathrm{in}(s, \mathrm{suchthat}(R, \mathrm{lambda}s\mathrm{in}(s, S))), \mathrm{notin}(f(s), T)))$

Source Code:

```<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<csymbol cd="relation1">eq</csymbol>
<apply>
<csymbol cd="logic1">not</csymbol>
<bind>
<csymbol cd="quant1">forall</csymbol>
<bvar>
<ci>s</ci>
</bvar>
<apply>
<csymbol cd="logic1">implies</csymbol>
<apply>
<csymbol cd="set1">in</csymbol>
<ci>s</ci>
<apply>
<csymbol cd="set1">suchthat</csymbol>
<ci>R</ci>
<bind>
<csymbol cd="fns1">lambda</csymbol>
<bvar>
<ci>s</ci>
</bvar>
<apply>
<csymbol cd="set1">in</csymbol>
<ci>s</ci>
<ci>S</ci>
</apply>
</bind>
</apply>
</apply>
<apply>
<csymbol cd="set1">in</csymbol>
<apply>
<ci>f</ci>
<ci>x</ci>
</apply>
<ci>T</ci>
</apply>
</apply>
</bind>
</apply>
<bind>
<csymbol cd="quant1">exists</csymbol>
<bvar>
<ci>s</ci>
</bvar>
<apply>
<csymbol cd="logic1">and</csymbol>
<apply>
<csymbol cd="set1">in</csymbol>
<ci>s</ci>
<apply>
<csymbol cd="set1">suchthat</csymbol>
<ci>R</ci>
<bind>
<csymbol cd="fns1">lambda</csymbol>
<bvar>
<ci>s</ci>
</bvar>
<apply>
<csymbol cd="set1">in</csymbol>
<ci>s</ci>
<ci>S</ci>
</apply>
</bind>
</apply>
</apply>
<apply>
<csymbol cd="set1">notin</csymbol>
<apply>
<ci>f</ci>
<ci>s</ci>
</apply>
<ci>T</ci>
</apply>
</apply>
</bind>
</apply>
[/itex]```