If P, Q, R are subsets of the universal set U, then (P ∩ Q ∩ R) ∪ (Pc∩ Q ∩ R) ∪Qc∪Rc is
A
Qc∪Rc
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
P ∪Qc∪Rc
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Pc∪Qc∪Rc
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
U
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is D U The given set theory expression can be convert in to equivalent boolean algebra expression follows:
(p ∩ q ∩ r) ∪ (pc∩ q ∩ r) ∪qc∪rc
= pqr + p'qr + q' + r'
= qr + (p + P') + q' + r'
= qr + q' + r'
=(q+q').(r+q')+r'
= r + q' + r'
= r + r' + q'
= 1 + q'
= 1 = U