Explanation Approach: A disjunction is a proposition of the form “ p or q ” and is represented symbolically by p ∨ q . The disjunction p ∨ q is false if both p and q are false; it is true in all other cases. A conditional statement is a proposition of the form “if p , then q ” and its represented symbolically by p → q . A tautology is a statement that is always true. A contradiction is a statement that is always false. Calculation: Construct the truth table for the expression. p q r ( p → q ) ( q → r ) ( p → r ) ( p → q ) ∨ ( q → r )

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ISBN: 9781337496094

Author: Tan

Publisher: CENGAGE C

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Chapter A.4, Problem 17E

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The statement [(p→q)∨(q→r)]→(p→r) is a tautology, a contradiction, or neither.

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Chapter A.4, Problem 16E

Chapter A.4, Problem 18E

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The statement [ ( p → q ) ∨ ( q → r ) ] → ( p → r ) is a tautology, a contradiction, or neither.

Solution Summary: The author explains that the statement (pto q) is neither a tautology or contradiction.

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The statement [(p→q)∨(q→r)]→(p→r) is a tautology, a contradiction, or neither.

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Chapter A Solutions