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Math Help - help me to transalate this using logical operator

  1. #1
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    help me to transalate this using logical operator

    P(x): x is a pen, x element of objects
    C(x): x is a cap, x element of objects
    R(x): x is red in color, x element objects
    L(x,y): x likes y, x element of people, y element of objects

    Question 1: John likes all red caps
    Question 2: At least two people like all red objects
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  2. #2
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    1)  \left( {\forall x} \right)\left[ {\left( {C(x) \wedge R(x)} \right) \Rightarrow L(John,x)} \right]  <br />

    2)  \left( {\exists x} \right)\left( {\exists y} \right)\left[ {x \ne y \wedge \left( {\forall z} \right)\left[ {R(z) \Rightarrow \left( {L(x,z) \wedge L(y,z)} \right)} \right]} \right] <br />
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