The given logical expression is \((p \land q) \Rightarrow p\). This can be interpreted as:

"If **p** and **q** are both true, then **p** must also be true."

### Truth Table Analysis:

Let's create a truth table to analyze the expression:

| p    | q    | p ∧ q | (p ∧ q) ⇒ p |
|:----:|:----:|:-----:|:-----------:|
| T    | T    |   T   |      T      |
| T    | F    |   F   |      T      |
| F    | T    |   F   |      T      |
| F    | F    |   F   |      T      |

### Explanation:

1. **When both p and q are true (T)**, the expression evaluates to true (T), because \( p \) is also true.
2. **When p is true and q is false (F)**, the conjunction \( p \land q \) is false, and since the implication \( \Rightarrow \) holds true whenever the premise is false, the expression evaluates to true.
3. **When p is false and q is true**, the conjunction \( p \land q \) is false, so the implication evaluates to true.
4. **When both p and q are false**, the conjunction is false, and so the implication is also true.

Thus, the entire expression is **always true**, making it a **tautology**.

Do you have any questions or would you like more details?

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**Relative questions:**
1. What is a tautology in logic?
2. How do truth tables work in propositional logic?
3. Can implications be true when the premise is false?
4. What is the difference between conjunction and implication?
5. How would the truth table change for the expression \( p \Rightarrow q \)?

**Tip:** In logic, an implication is always true when the premise is false, regardless of the conclusion.

Explore the logical expression (p ∧ q) ⇒ p with a step-by-step analysis using truth tables. Learn key concepts like conjunction, implication, and tautology. Suitable for students in Grades 9-12 studying propositional logic.

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