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Question

Let p,q,r denote the arbitary statements then the logical equivalance of the statement p(qr) is 


A
(pq)r
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B
(pq)(pr)
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C
(pq)(pr)
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D
(pq)(pr)
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Solution

The correct option is D (pq)(pr)
pqrqrp(qr)pq(pq)rpqprpqpr(pq)(pr)(pq)(pr)(pq)(pr)TTTTTTTTTFFTFFTTFTTTFTFFTTFTTFTTTTTFTTFTTFTFFFFTFFFTTFFFFTTTTTTTTTTTTTFTFTTTFTTTTTTTFFTTTFTTTTTTTTFFFFTFTTTTTTTT

From the above table, it is clear that p(qr) is equivalent to (pq)(pr).

Alternate :
p(qr)=p(qr)
=(pq)(pr)
=(pq)(pr)

Mathematics

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