...
Computer-Networks
February 8, 2024
GATE 2008
February 8, 2024
Computer-Networks
February 8, 2024
GATE 2008
February 8, 2024

GATE 2008

Question 2

If P, Q, R are subsets of the universal set U, then (P∩Q∩R) ∪ (Pc∩Q∩R) ∪ Q∪ Rc is

A
Qc ∪ Rc
B
P ∪ Qc ∪ Rc
C
Pc ∪ Qc ∪ Rc
D
U
Question 2 Explanation: 
Given,
(P∩Q∩R)∪(Pc∩Q∩R)∪Qc∪Rc
It can be written as the p.q.r + p’.q.r +q’ + r’
=> (p+p’).q.r + q’ + r’
=> q.r + (q’+r’)
=> q.r + q’ + r’ = 1 i.e., U
Correct Answer: D
Question 2 Explanation: 
Given,
(P∩Q∩R)∪(Pc∩Q∩R)∪Qc∪Rc
It can be written as the p.q.r + p’.q.r +q’ + r’
=> (p+p’).q.r + q’ + r’
=> q.r + (q’+r’)
=> q.r + q’ + r’ = 1 i.e., U

Leave a Reply

Your email address will not be published. Required fields are marked *