GATE | GATE CS 2008 | Question 2

If P, Q, R are subsets of the universal set U, then 2 

(A) Qc U Rc
(B) P U Qc U Rc
(C) Pc U Qc U Rc
(D) U

Answer: (D)

Explanation:  (P\cap Q \cap r)\cup (P^{'}\cap Q \cap R)\cup(Q^{'} \cup R^{'}) \hspace{0.1cm}where\hspace{0.1cm}'\hspace{0.1cm}denotes\hspace{0.1cm}complement  = (P\cup P^{'}) \cap ((Q\cap R))\cup(Q^{'}\cup R^{'}))  = U \cap ((Q\cap R)\cup(Q\cap R^{'}))  = U \cap U  = U(universal set)

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