If p is false, what is the truth value of ~~p?truefalsecannot be determinedSubmit

1. Break Down the Problem

We need to determine the truth value of the expression $~~p$ when $p$ is false.

2. Relevant Concepts

The expression $~~p$ represents the double negation of $p$. According to the rules of logic:

• If $p$ is false, then $~p$ (the negation of $p$) will be true.
• Applying negation again, $~~p$ will revert the truth value back to that of $p$.

3. Analysis and Detail

1. Given $p$ is false: $p = \text{false}$
2. The first negation of $p$: $~p = \text{true} \quad \text{(since negating false results in true)}$
3. The second negation: $~~p = p = \text{false}$

4. Verify and Summarize

Therefore, after applying the double negation, $~~p$ results in the original truth value of $p$, which is false.

Final Answer

The truth value of $~~p$ is false.