logic5

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

<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="set1">in</csymbol>
        <ci>s</ci>
        <ci>S</ci>
      </apply>
    </bind>
  </apply>
</math>

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