Question

Prove that `(not(p rarr q) ^^ (p harr notq)) harr ((p ^^ notq))`?

Answer 1

We can build a truth table for each of the statements.

Since the truth values for:

`not(p rarr q) ^^ (p harr notq)` and `(p ^^ notq)`

are exactly the same for all possible combinations of truth values of `p` and `q`, then

`(not(p rarr q) ^^ (p harr notq)) harr ((p ^^ notq))`

is a tautology and therefore the two propositions are equivalent. QED