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If the statements p and q are true and the statement r and s are false, find the truth values of :
(1) `~[(pvvq)^^~r]^^{[(~pvvq)vv(~r)]vvs}`
(2) `p^^[q^^(~p^^r)vv~s]vv~r`.

Text Solution

Verified by Experts

Truth values of p and q are T and truth values of r and s are F.
(1) `~[(pvvq)^^~r]^^{[(~pvvq)^^(~r)]vvs}`
`-=~[(TvvT)^^~F]^^{[(~TvvT)vv(~F)]vvF}`
`-=~(T^^T)^^{[(FvvT)vvT]vvF}`
`-=~T^^{(TvvT)vvF}`
`-=F^^(TvvF)" "-=F^^T-=F`
Hence the truth value of the given statement is false.
(2) `p^^[q^^(~p^^r)vv~s]vv~r`
`-=~[(TvvT)^^~F]^^{[(~TvvT)vv(~F)]vvF}`
`-=~(T^^T)^^{[(FvvT)vvT]vvF}`
`-=T^^[(T^^F)vvT]vvT`
`-=T^^(FvvT)vvT-=TvvT^^T-=TvvT-=T`
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