GATE | GATE CS 2008 | Question 2
If P, Q, R are subsets of the universal set U, then
(A)
Qc U Rc
(B)
P U Qc U Rc
(C)
Pc U Qc U Rc
(D)
U
Answer: (D)
Explanation:
The given set theory expression can be converted into an equivalent boolean algebra expression as follows:
=p.q.r + p’.q.r + q’+r’
=qr(p+p’)+q’+r’
=qr+q’+r’
=(q+q’) . (r+q’) +r’
=r+r’+q’
=1+q’
=1
=U
Option (D) is correct
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Last Updated :
16 Feb, 2018
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