How do you create a truth table to prove that for any statement, p,~(~p) equals p?

If is true, then is false, which in turn means is true.

If is false, then is true, and so is false.

So, because in both cases, the statement is a tautology (always true).

If you were to put this in a table, you would have one column each for . In the first column () you can think of as an independent variable that can only take two values, true and false. In the next column (), you would negate the value in the previous column. And so on.

It should roughly look like this:

p ... ~p ... ~(~p)
T ...  F  ...    T
F ...  T  ...    F