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Use a truth table to determine whether the two statements are equivalent. p→-q, q→p

Use a truth table to determine whether the two statements are equivalent. p→-q, q→p

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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8.
**Determine Equivalence of Logical Statements Using Truth Tables** To determine whether the two statements \( p \rightarrow q \) and \( q \rightarrow p \) are equivalent, we can use truth tables. ### Construct a Truth Table for \( p \rightarrow q \): | p | q | \( p \rightarrow q \) | |-----|-----|-----------------------| | T | T | | | T | F | | | F | T | | | F | F | | ### Construct a Truth Table for \( q \rightarrow p \): | p | q | \( q \rightarrow p \) | |-----|-----|-----------------------| | T | T | | | T | F | | | F | T | | | F | F | | ### Are the statements equivalent? - ☐ The statements are equivalent. - ☐ The statements are not equivalent. Use the completed truth tables to determine if the statements are equivalent by comparing the values in the columns for \( p \rightarrow q \) and \( q \rightarrow p \). If the values are the same in each corresponding row, the statements are equivalent; otherwise, they are not.
Transcribed Image Text:**Determine Equivalence of Logical Statements Using Truth Tables** To determine whether the two statements \( p \rightarrow q \) and \( q \rightarrow p \) are equivalent, we can use truth tables. ### Construct a Truth Table for \( p \rightarrow q \): | p | q | \( p \rightarrow q \) | |-----|-----|-----------------------| | T | T | | | T | F | | | F | T | | | F | F | | ### Construct a Truth Table for \( q \rightarrow p \): | p | q | \( q \rightarrow p \) | |-----|-----|-----------------------| | T | T | | | T | F | | | F | T | | | F | F | | ### Are the statements equivalent? - ☐ The statements are equivalent. - ☐ The statements are not equivalent. Use the completed truth tables to determine if the statements are equivalent by comparing the values in the columns for \( p \rightarrow q \) and \( q \rightarrow p \). If the values are the same in each corresponding row, the statements are equivalent; otherwise, they are not.
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