I am working on a tautology question and understand most of the answer except for one part. I need to show that the following is a tautology:

<=> means equivalent

Code: Select all

`p -> [(~p) -> q)] `

<=> ~p v [~(~p v q)] <- this line - why the first ~? How do I get it? Is it because of the already existing ~p?

<=> ~p v [ p v q]

<=> (~p v p) v q

<=> T v q

<=> t

I don't understand the reason for the first ~, the one in in this line "<=> ~p v [~(~p v q)]". I realize I need it to complete the exercise but I don't understand how I get it. Can someone please help me to understand this?

Thanks for any help,

Tony