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Which of the following statement is a ta...

Which of the following statement is a tautology?

A

(~p`vv`~q)`vv`(p`vv`~q)

B

(~p`vv`~q)`wedge` (p`vv`~q)

C

~p`wedge`(~p`vv`~q)

D

~q`wedge` (~p`vv`~q)

Text Solution

Verified by Experts

The correct Answer is:
A
(~ p`vv` ~ q) `vv` (p `vv` ~ q)
`-=` (~q `vv` ~ p)`vv` (~q `vv` p) (by commutative law )
`-=`~q `vv` (~p `vv` p)
`-=` ~ q `vv` t , (` because` (~ p `vv` p) `-=` t , t is tautology )
`-=t`
Hence (~p`vv` ~ q) `vv` (p `vv` ~ q) is a tautology
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