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Let's solve the problem step by step.

The expression given is \((q \rightarrow p) \lor \sim r\), where:
- \(q \rightarrow p\) is the implication (if \(q\), then \(p\)).
- \(\lor\) represents the logical OR.
- \(\sim r\) represents the negation of \(r\).

We'll construct the truth table for all possible combinations of \(p\), \(q\), and \(r\). There are 3 variables, so we'll have \(2^3 = 8\) rows.

### Truth Table:

| \(p\) | \(q\) | \(r\) | \(q \rightarrow p\) | \(\sim r\) | \((q \rightarrow p) \lor \sim r\) |
|:----:|:----:|:----:|:---------------:|:------:|:------------------------:|
|  T   |  T   |  T   |       T         |   F    |           T              |
|  T   |  T   |  F   |       T         |   T    |           T              |
|  T   |  F   |  T   |       T         |   F    |           T              |
|  T   |  F   |  F   |       T         |   T    |           T              |
|  F   |  T   |  T   |       F         |   F    |           F              |
|  F   |  T   |  F   |       F         |   T    |           T              |
|  F   |  F   |  T   |       T         |   F    |           T              |
|  F   |  F   |  F   |       T         |   T    |           T              |

### Explanation:
1. **\(q \rightarrow p\)** is true if \(q\) is false or \(p\) is true (because an implication with a false antecedent is true, and if the consequent is true, the implication is true).
2. **\(\sim r\)** negates the truth value of \(r\).
3. The result of **\((q \rightarrow p) \lor \sim r\)** is true if at least one of \(q \rightarrow p\) or \(\sim r\) is true.

Would you like more details or have any questions?

### Related Questions:
1. How do logical implications differ from other logical operations?
2. Can you construct a truth table for \( (p \land \sim q) \lor r \)?
3. What is the result of \( q \rightarrow p \) when both \( p \) and \( q \) are false?
4. How does negation affect the outcome of a logical statement?
5. What are some practical uses of truth tables in computer science?

### Tip:
To evaluate logical expressions, always start with inner operations (like negations) and then proceed to evaluate compound expressions step by step.

Construct a truth table for (q → p) ∨ ~r. Use T for true and F for false.

Learn how to construct a truth table for the expression (q → p) ∨ ~r. This exercise involves understanding logical operations such as implication, negation, and disjunction. Step-by-step instructions provided for students in Grades 10-12.

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