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Find logical validity Hypothesis = p=>q,p=>r and Conclusion = p=>(q and r)

Your problem `->` logical validity Hypothesis = p=>q,p=>r and Conclusion = p=>(q and r)

Hypothesis :


Conclusion :
`S : p=>(q^^r)`

TTT T `T=T=>T` T `T=T=>T` T `T=T^^T`critical row T `T=T=>T`
TTF T `T=T=>T` F `F=T=>F` F `F=T^^F` F `F=T=>F`
TFT F `F=T=>F` T `T=T=>T` F `F=F^^T` F `F=T=>F`
TFF F `F=T=>F` F `F=T=>F` F `F=F^^F` F `F=T=>F`
FTT T `T=F=>T` T `T=F=>T` T `T=T^^T`critical row T `T=F=>T`
FTF T `T=F=>T` T `T=F=>F` F `F=T^^F`critical row T `T=F=>F`
FFT T `T=F=>F` T `T=F=>T` F `F=F^^T`critical row T `T=F=>F`
FFF T `T=F=>F` T `T=F=>F` F `F=F^^F`critical row T `T=F=>F`

The conclusion `(S)` is true in all critical rows. So the argument is logically valid.

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