Explanation Given: The given compound statement is, ( q ∧ p ) → ( ∼ r ∨ p ) Description: The disjunction p ∨ q joins the two statements with the word “or”. The disjunction is true if at least one of the components of the disjunction is true. The disjunction is false if both the statements are false. The conjunction p ∧ q joins the two statements with the word “and”. The conjunction is true if both the components of the conjunction is true. The conjunction is false if at least one of the statements is false. The conditional statement p → q is made up of two statements p and q . It follows the form “If p , then q ”. If the statement p is true the conditional statement will depend on whether the statement q is true or false. If the statement p is false the conditional statement will be false and does not depend on whether the statement q is true or false. The negation ∼ p is the opposite of the statement p . If the component of the statement is true the negation of statement is false and vice-versa. Approach: The given compound statement is, ( q ∧ p ) → ( ∼ r ∨ p ) There are 3 letters in the given compound statement. So, there will be 2 3 = 8 rows in the truth table. There will be seven columns in the truth table. One column for the letter p . Second column for the letter q . Third column for letter r . Fourth column for negation ∼ r . Fifth column for conjunction ( q ∧ p ) . Sixth column for disjunction ( ∼ r ∨ p ) . Seventh column for conditional statement ( q ∧ p ) → ( ∼ r ∨ p )

8th Edition

ISBN: 9780357425831

Author: Johnson

Publisher: CENGAGE L

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Chapter 1.CR, Problem 24CR

To determine

To construct:

The truth table for the given compound statement.

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To construct: The truth table for the given compound statement.

Solution Summary: The author explains the truth table for the given compound statement. The disjunction is true if both the components of the conjunction are true.