# Math Help - help me to transalate this using logical operator

1. ## 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

2. 1) $\left( {\forall x} \right)\left[ {\left( {C(x) \wedge R(x)} \right) \Rightarrow L(John,x)} \right]
$

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]
$