Question

Please help me solve​

Answer 1

`(P\cup Q)\cap (P\cap Q^c)=((P\cup Q)\cap P)\cap Q^c=P\cap Q^C\Rightarrow \text{C}`

I guess those pluses are there by a mistake.

Answer 2

Answer and explanation:

The equivalent set to (P∪Q)∩(P∩Qc) is P. Here’s the proof:

(P∪Q)∩(P∩Qc) = Distributive Law [(P∪Q)∩P]∩[(P∪Q)∩Qc] = Identity Law [P∩P]∩[(P∪Q)∩Qc] = Absorption Law P∩[(P∪Q)∩Qc] = Distributive Law [P∩(P∪Q)]∩[P∩Qc] = Absorption Law P∩[P∩Qc] = Associative Law (P∩P)∩Qc = Idempotent Law P∩Qc

So, the correct answer is C. P.