Explanation Given Information: The provided statement is ( p ∨ q ) ∨ r ≡ p ∨ ( q ∨ r ) . Formula used: The symbol ( ≡ ) implies logical equivalence which means that the right-hand side statement is logically equivalent to the left-hand side statement and both the statement have the same truth values. The symbol ∧ implies conjunction which means that if both the statements are true then the conclusion of the statements will be true otherwise false. The symbol ∨ implies disjunction which means that if either of the two statements is true or both statements are true then the conclusion of the statements will be true. Proof: Consider the statement ( p ∨ q ) ∨ r ≡ p ∨ ( q ∨ r ) . There are three variables p , q, and r . So, the first three columns of the table are for the three variables, the fifth column represents ( p ∨ q ) ∨ r and the seventh column represents p ∨ ( q ∨ r ) as the given statement requires ( p ∨ q ) ∨ r ≡ p ∨ ( q ∨ r )

7th Edition

ISBN: 8220103612005

Author: Costenoble

Publisher: CENGAGE L

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Chapter A, Problem 70E

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To prove: The logical equivalence of (p∨q)∨r≡p∨(q∨r) by use of the truth tables.

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Chapter A, Problem 69E

Chapter A, Problem 71E

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Chapter A Solutions

EBK FINITE MATH AND APPLIED CALCULUS

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To prove: The logical equivalence of ( p ∨ q ) ∨ r ≡ p ∨ ( q ∨ r ) by use of the truth tables.

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To prove: The logical equivalence of (p∨q)∨r≡p∨(q∨r) by use of the truth tables.

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Chapter A Solutions