Question

I don’t understand this and need help! Please help!

Answer 1

`p\implies\sim q` is true when
`p` is false, or when both
`p` and
`\sim q` are true.

Similarly,
`q\implies\sim p` is true when
`q` is false, or when both
`q` and
`\sim p` are true.

It seems that you are given that
`p\implies\sim q` and
`q\implies\sim p`. According to the truth table given above, these can both be true only when one of
`p,q` is true and the other is false.

On the other hand,
`p\lor q` is true when either or both of
`p` or
`q` is true. This is satisfied by the implications in the hypothesis, so
`p\lor q` must be true.