K Use a truth table to determine whether the two statements are equivalent. (pv q) Ar and pv (q^r) Construct the truth table. PT р T T T F T LL F LL q r (p v q) ^ r T T F T F T T T F F T F F F TI F TI TI LL LL pv (q^r) Choose the correct answer below. O The statements are equivalent. O The statements are not equivalent. www

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Construct a Truth Table**

To determine whether the two statements are equivalent, we need to construct a truth table for:

\((p \lor q) \land r\) and \(p \lor (q \land r)\).

| p   | q   | r   | \((p \lor q) \land r\) | \(p \lor (q \land r)\) |
|-----|-----|-----|----------------------------|---------------------------|
| T   | T   | T   |                            |                           |
| T   | T   | F   |                            |                           |
| T   | F   | T   |                            |                           |
| T   | F   | F   |                            |                           |
| F   | T   | T   |                            |                           |
| F   | T   | F   |                            |                           |
| F   | F   | T   |                            |                           |
| F   | F   | F   |                            |                           |

**Choose the correct answer below:**

- ☐ The statements are equivalent.
- ☐ The statements are not equivalent.

Fill in the truth table to analyze the logical equivalence between the given statements.
Transcribed Image Text:**Construct a Truth Table** To determine whether the two statements are equivalent, we need to construct a truth table for: \((p \lor q) \land r\) and \(p \lor (q \land r)\). | p | q | r | \((p \lor q) \land r\) | \(p \lor (q \land r)\) | |-----|-----|-----|----------------------------|---------------------------| | T | T | T | | | | T | T | F | | | | T | F | T | | | | T | F | F | | | | F | T | T | | | | F | T | F | | | | F | F | T | | | | F | F | F | | | **Choose the correct answer below:** - ☐ The statements are equivalent. - ☐ The statements are not equivalent. Fill in the truth table to analyze the logical equivalence between the given statements.
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