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Use a truth table to determine whether the two statements are 12) -p ^-q and -(p Vq) equivalent.

Use a truth table to determine whether the two statements are 12) -p ^-q and -(p Vq) equivalent.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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The image contains instructions and diagrams for constructing truth tables to determine logical equivalence. **Instructions:** - Construct a truth table for the given statement. - Read the statement carefully. - Use a truth table to determine whether the two statements are equivalent. **Exercises:** 1. **Exercise 11:** Construct a truth table for the statement \( (q \rightarrow p) \land \neg q \). **Table (a):** - Variables: \( p \), \( q \) - Expressions: \( q \rightarrow p \), \( (q \rightarrow p) \land \neg q \) Truth table with possible combinations: - T T T F F T - T F F F F T - F T T F T F - F F T T F T 2. **Exercise 12:** Determine if \( p \land \neg q \) and \( \neg (p \lor q) \) are equivalent. **Table (b):** - Variables: \( p \), \( q \) - Expressions: \( \neg q \), \( p \land \neg q \), \( \neg (p \lor q) \) Truth table with possible combinations: - T T F F F F - T F T T F F - F T F F F T - F F T F F F These tables are systematically filled out to aid in verifying the logical equivalences of the given statements.
Transcribed Image Text:The image contains instructions and diagrams for constructing truth tables to determine logical equivalence. **Instructions:** - Construct a truth table for the given statement. - Read the statement carefully. - Use a truth table to determine whether the two statements are equivalent. **Exercises:** 1. **Exercise 11:** Construct a truth table for the statement \( (q \rightarrow p) \land \neg q \). **Table (a):** - Variables: \( p \), \( q \) - Expressions: \( q \rightarrow p \), \( (q \rightarrow p) \land \neg q \) Truth table with possible combinations: - T T T F F T - T F F F F T - F T T F T F - F F T T F T 2. **Exercise 12:** Determine if \( p \land \neg q \) and \( \neg (p \lor q) \) are equivalent. **Table (b):** - Variables: \( p \), \( q \) - Expressions: \( \neg q \), \( p \land \neg q \), \( \neg (p \lor q) \) Truth table with possible combinations: - T T F F F F - T F T T F F - F T F F F T - F F T F F F These tables are systematically filled out to aid in verifying the logical equivalences of the given statements.
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