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GATE | GATE CS 2008 | Question 2

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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:

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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