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This is a propositional logic statement:

**P → (Q → P ∧ Q)**

Let’s solve it step-by-step:

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### Step 1: Understand the logical formula
- **P → (Q → P ∧ Q)** means:  
  "If P is true, then if Q is true, P ∧ Q must also be true."

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### Step 2: Break it down using logical equivalences  
1. **Implication rewrite**: The implication **P → X** is equivalent to **¬P ∨ X**.  
   Rewrite the formula:  
   \[
   ¬P ∨ (¬Q ∨ (P ∧ Q))
   \]

2. **Distribute the parentheses**:  
   Simplify **¬Q ∨ (P ∧ Q)** using the distributive property:  
   \[
   ¬Q ∨ P ∨ Q
   \]

   (This step is true because **¬Q ∨ (P ∧ Q)** means either ¬Q is true, or P and Q are both true. Simplifying this leads to **¬Q ∨ P ∨ Q**.)

3. Combine terms:  
   Notice that **¬P ∨ (¬Q ∨ P ∨ Q)** can be combined further:  
   \[
   ¬P ∨ P ∨ ¬Q ∨ Q
   \]

   - **¬P ∨ P** simplifies to **True** (a tautology).  
   - **¬Q ∨ Q** also simplifies to **True** (a tautology).  

   So the entire expression simplifies to **True**.

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### Final Answer:
The statement **P → (Q → P ∧ Q)** is always **True** (a tautology).

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Would you like me to explain any specific part of the solution further?

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### Related Questions:
1. What are the rules for simplifying logical expressions?
2. How does the implication **P → Q** translate into logical equivalence?
3. Why does **¬P ∨ P** simplify to a tautology (True)?
4. What is the significance of a tautology in propositional logic?
5. How can truth tables be used to verify tautologies?

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### Tip:
When solving logical expressions, always start by rewriting implications as disjunctions (**¬P ∨ Q**) to make simplifications easier!

Learn how to simplify the logical expression P → (Q → P ∧ Q) step-by-step. This problem involves key concepts of propositional logic, including implications, logical equivalences, and tautologies. Suitable for advanced high school or university-level students.

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