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Let's break down the logic propositions step by step and evaluate them based on the given values of \( p = T \), \( q = T \), and \( r = F \).

### Proposition 1: \( (q \lor r) \rightarrow \neg p \)

- \( q \lor r \): 
  - \( q = T \) and \( r = F \), so \( q \lor r = T \).
  
- \( \neg p \): 
  - \( p = T \), so \( \neg p = F \).

- \( (q \lor r) \rightarrow \neg p \): 
  - \( T \rightarrow F \) is **false** (since the only false case for implication is when the first part is true and the second part is false).

So, Proposition 1 evaluates to **false**.

### Proposition 2: \( \neg r \leftrightarrow (p \land q) \)

- \( \neg r \): 
  - \( r = F \), so \( \neg r = T \).
  
- \( p \land q \): 
  - \( p = T \) and \( q = T \), so \( p \land q = T \).
  
- \( \neg r \leftrightarrow (p \land q) \): 
  - \( T \leftrightarrow T \) is **true** (since the biconditional is true when both sides have the same truth value).

So, Proposition 2 evaluates to **true**.

### Conclusion:
- Proposition 1 is **false**.
- Proposition 2 is **true**.

Now, let's match this with the given options:

- **Option C** correctly states that \( (q \lor r) \rightarrow \neg p = F \) and \( \neg r \leftrightarrow (p \land q) = T \).

So, the correct answer is **C**.

Would you like more details or further clarification? Here are some related questions you might find useful:

1. What is the difference between implication and biconditional statements?
2. How do truth tables work for logical operators like \(\lor\), \(\land\), and \(\rightarrow\)?
3. Can a proposition be true and false under different interpretations?
4. What is the only case where an implication is false?
5. How can we represent logical operations using set theory?

**Tip:** When evaluating implications, remember that the implication is false only if the premise is true and the conclusion is false.

p = T, q = T, r = F. Select the correct truth values for the two propositions: (q ∨ r) → ¬p and ¬r ↔ (p ∧ q).

Evaluate the truth values of the propositions (q ∨ r) → ¬p and ¬r ↔ (p ∧ q) given p = T, q = T, and r = F. This solution explains the logical steps involved in solving the problem, focusing on implications and biconditionals. Suitable for students in Grades 9-12.

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