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GATE | GATE CS 2008 | Question 2

Last Updated : 16 Feb, 2018

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Discuss

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

(A) Q^c U R^c
(B) P U Q^c U R^c
(C) P^c U Q^c U R^c
(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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