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Negation of the statement p to ( q ^^ ...

Negation of the statement `p to ( q ^^ r)` is

A

` ~ p to ~ ( q vv r)`

B

` ~ p to ~ ( q ^^ r)`

C

` ( q ^^ r) to p`

D

` p ^^ ( ~ q vv ~ r)`

Text Solution

Verified by Experts

The correct Answer is:
D
we know that
` ~ ( p vv q) cong p ^^ ~ q`
` ~ ( p vv q) cong p ^^ ~ q`
` ~ ( p to ( q ^^ r) cong p ^^ ( ~ ( q ^^ r))`
` cong p ^^ ( ~ q vv ~ r) `[ By De' Morgan's laws]
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