3. (20 points) The binary relation R is defined on Z such that aRb if and only if a and b have the same parity. (Two integers have the same parity if they are both odd or both even.) Determine whether R is reflexive, symmetric, antisymmetric and/or transitive. (Steps required) 4. (10 points) Without drawing a Venn diagram, prove or disprove the following statement: P(ST)=P(S)P(T) for any non-empty sets S and T. (Steps required).

1. 3. (20 points) The binary relation R is defined on Z such that aRb if and only if a and b have the
same parity. (Two integers have the same parity if they are both odd or both even.) Determine
whether R is reflexive, symmetric, antisymmetric and/or transitive. (Steps required) 4. (10 points)
Without drawing a Venn diagram, prove or disprove the following statement: P(ST)=P(S)P(T) for
any non-empty sets S and T. (Steps required)