Verify that [p?(q ?r)] ? [(p?q)?(p?r)] is a tautology. Solution p...q...r... [p-

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p...q...r... [p-->(q-->r)]...[(p-->q)-->(p-->r)]. . . . . [..]-->[..] T...T...T..........T............ ............ T............ ....... T T...T...F..........F............ .......does not matter . .. T T...F...T..........T............ ............ T.......... .......... T T...F...F..........T............ ............ T.......... .......... T F...T...T..........T............ ............ T......... ........... T F...T...F..........T............ ............ T.......... .......... T F...F...T..........T............ ............ T........... ......... T F...F...F..........T............ ............ T............ ........ T Rightmost column is all T, therefore expression is tautology.

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