Question

Create a truth table and prove that for any statement p, ~(~p) equals p.

Answer 1

$p=T\implies\sim p=F\implies\sim(\sim p)=T$
$p=F\implies\sim p=T\implies\sim(\sim p)=F$

In either case, we have $p\equiv\sim(\sim p)$, so the statement is always true (a tautology).

Answer 2

Answer:

The required truth table is

p                  ~p              ~(~p)

T                   F                  T

F                   T                  F

Step-by-step explanation:

If p is true, then ~p is false. The sign ~(~p) means the statement "~p is false" is false. So, we can say that ~(~p) means p is true.

If p is false, then ~p is true. The sign ~(~p) means the statement "~p is true" is false. So, we can say that ~(~p) means p is false.

The required truth table is

p                  ~p              ~(~p)

T                   F                  T

F                   T                  F

From the above truth table it is clear that

~(~p) = p

Hence proved.