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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:

| \( p \) | \( q \) | \( p \implies q \) | \( p \implies (p \implies q) \) |
|--------|--------|--------------------|---------------------------------|
|   T    |   T    |         T          |                T                |
|   T    |   F    |         F          |                F                |
|   F    |   T    |         T          |                T                |
|   F    |   F    |         T          |                T                |

### 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!

Buatlah tabel kebenaran dari setiap pernyataan majemuk berikut: p => (p => q)

Explore how to construct a truth table for the logical expression p => (p => q). This problem focuses on logical implications and truth values, providing a step-by-step breakdown of each case. Suitable for students in Grades 10-12.

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