https://file.aiquickdraw.com/mathbot/file/17269601500942e1sn0w5.jpg

The expression in the image is:

\[
(p \land q) \to p
\]

This is a logical implication statement in propositional logic. Let's break it down:

- \( p \land q \): This means "p AND q." It's true if both \( p \) and \( q \) are true, and false otherwise.
- \( \to \): This is the implication operator, meaning "if ... then."
- The whole expression \( (p \land q) \to p \) reads as "if \( p \land q \) is true, then \( p \) is true."

### Truth Table
We can construct the truth table to see when this statement holds.

| \( p \) | \( q \) | \( p \land q \) | \( (p \land q) \to p \) |
|--------|--------|----------------|------------------------|
|   T    |   T    |        T       |           T            |
|   T    |   F    |        F       |           T            |
|   F    |   T    |        F       |           T            |
|   F    |   F    |        F       |           T            |

The expression is always true, except when \( p \land q \) is true and \( p \) is false, which doesn't occur in the truth table. Therefore, \( (p \land q) \to p \) is a **tautology** (always true).

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What does \( p \lor q \) represent in propositional logic?
2. How do you construct the truth table for \( p \lor q \to r \)?
3. What is the contrapositive of \( (p \land q) \to p \)?
4. Can you show an example where \( (p \lor q) \to p \) is false?
5. What is the negation of the implication \( (p \land q) \to p \)?

**Tip:** In logic, an implication \( A \to B \) is false only when \( A \) is true and \( B \) is false.

Explore the logical expression (p ∧ q) → p, a tautology in propositional logic. This page breaks down the truth table for this implication, explaining the conditions under which it holds true. Suitable for high school students learning about mathematical logic.

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