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Q. The number of values of r{p,q,p,q} for which ((pq)(rq))((pr)q) is a tautology, is :

JEE MainJEE Main 2023Mathematical Reasoning

Solution:

((pq)(rq))((pr)q)
We know, pq is equivalent to
pq
((pq)(rq))((pr))q))
(pqrq)(prq)
(prt)(prq)
(t)(prq)
For this to be tautology, (prq) must be always true which follows for r=∼p or r=q.