The problem asks to create a truth table for the compound statement $p \implies (p \implies q)$.

Let's break down the logical expression and create a truth table step by step.

The components involved:

• $p$
• $q$
• $p \implies q$
• $p \implies (p \implies q)$

Truth Table:

Explanation:

1. $p \implies q$ means that if $p$ is true, then $q$ must also be true. If $p$ is true and $q$ is false, the implication is false. In all other cases, it is true.
2. $p \implies (p \implies q)$ means that the implication itself is compared with $p$. If $p$ is false, the whole statement is automatically true. If $p$ is true, then the truth value of $(p \implies q)$ is checked to decide the final result.

Would you like more details on any specific part?

Here are five follow-up questions to consider:

1. How do we determine the truth values for implications?
2. What happens when both $p$ and $q$ are false in logical statements?
3. How does a truth table represent all possible cases?
4. Can compound statements include more than two propositions? How would you handle that?
5. How would you simplify a complex logical expression like $p \implies (p \implies q)$?

Tip: When working with implications, remember that an implication is always true unless the premise is true and the conclusion is false!