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Find truth table p or (q and r)=(p or q) and (p or r)

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Your problem `->` truth table p or (q and r)=(p or q) and (p or r)


To prove `pvv(q^^r)=(pvvq)^^(pvvr)`, we havet to first prepare the following truth table

`(1)``(2)``(3)``(4)=(2)^^(3)``(5)=(1)vv(4)``(6)=(1)vv(2)``(7)=(1)vv(3)``(8)=(6)^^(7)`
`p``q``r``q^^r``pvv(q^^r)``pvvq``pvvr``(pvvq)^^(pvvr)`
TTT T `T=T^^T` T `T=TvvT` T `T=TvvT` T `T=TvvT` T `T=T^^T`
TTF F `F=T^^F` T `T=TvvF` T `T=TvvT` T `T=TvvF` T `T=T^^T`
TFT F `F=F^^T` T `T=TvvF` T `T=TvvF` T `T=TvvT` T `T=T^^T`
TFF F `F=F^^F` T `T=TvvF` T `T=TvvF` T `T=TvvF` T `T=T^^T`
FTT T `T=T^^T` T `T=FvvT` T `T=FvvT` T `T=FvvT` T `T=T^^T`
FTF F `F=T^^F` F `F=FvvF` T `T=FvvT` F `F=FvvF` F `F=T^^F`
FFT F `F=F^^T` F `F=FvvF` F `F=FvvF` T `T=FvvT` F `F=F^^T`
FFF F `F=F^^F` F `F=FvvF` F `F=FvvF` F `F=FvvF` F `F=F^^F`


from this table, we can say that columns (5) and (8) are identical.
`:. pvv(q^^r)=(pvvq)^^(pvvr)`






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