https://file.aiquickdraw.com/mathbot/file/1728958509000zugxl9ss.jpg

The expression in the image is: \((p \Rightarrow q) \lor r\).

Let's break this down to construct the truth table:

1. \(p \Rightarrow q\) is a conditional statement that is false only when \(p\) is true and \(q\) is false, and true otherwise.
2. \(\lor\) represents the logical "or" operator, which is true if at least one of the operands is true.

We need to evaluate \((p \Rightarrow q) \lor r\) for all possible combinations of truth values for \(p\), \(q\), and \(r\).

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

- Column 4 shows the evaluation of \(p \Rightarrow q\) for each combination of \(p\) and \(q\).
- Column 5 shows the evaluation of \((p \Rightarrow q) \lor r\), which takes the result of \(p \Rightarrow q\) and combines it with \(r\) using logical "or."

Let me know if you'd like further explanation or have any questions!

### Related Questions:
1. How do you determine the truth value of a conditional statement like \(p \Rightarrow q\)?
2. What are the truth tables for other logical operations, such as "and" (\(\land\)) or "not" (\(\neg\))?
3. How would the truth table change if the expression used \(\land\) instead of \(\lor\)?
4. Can you explain the logical equivalence between \(\neg p \lor q\) and \(p \Rightarrow q\)?
5. How do logical operations apply in circuit design or programming conditions?

### Tip:
In truth tables, conditional statements (\(p \Rightarrow q\)) are true whenever \(p\) is false or when \(q\) is true.

Select the truth table for the following expression: (p ⇒ q) ∨ r

Learn how to construct the truth table for the logical expression (p ⇒ q) ∨ r. This problem covers key logic concepts, including conditional statements and the logical OR operator. Suitable for students in Grades 10-12.

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