GATE | GATE CS 2008 | Question 2

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:

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

Quiz of this Question
Please comment below if you find anything wrong in the above post