logic6

not (forall s in S where f(s) is in T) = (there exists s in S such that f(s) is not in T)

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

Author: Design Science, Inc. (E. Cannon, E. Tabacman, R.Miner)