Explanation 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 is true if both the components of the conjunction is true. The conjunction is false if at least one of the statements is false. 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 true 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. An argument having n premises P 1 , P 2 , P 3 , ... , P n and conclusion C can be represented by the conditional [ P 1 ∧ P 2 ∧ P 3 ∧ ... ∧ P n ] → C . An argument is valid if and only if the conditional [ P 1 ∧ P 2 ∧ P 3 ∧ ... ∧ P n ] → C is a tautology. Approach: Consider the argument p → q q → p ∴ p ↔ q . Therefore, the conditional for the argument is, [ ( p → q ) ∧ ( q → p ) ] → ( p ↔ q ) There are 2 letters in the given symbolic expression. So, there will be 2 2 = 4 rows in the truth table

11th Edition

ISBN: 9781337496094

Author: Tan

Publisher: CENGAGE C

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities.…

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Chapter A.5, Problem 9E

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The validity of the argument p→qq→p ∴p↔q.

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Chapter A.5, Problem 8E

Chapter A.5, Problem 10E

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To check: The validity of the argument p → q q → p ∴ p ↔ q .

Solution Summary: The author explains that the argument lpto q is valid, and the conjunction is false if both the statements are false.

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The validity of the argument p→qq→p ∴p↔q.

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Chapter A Solutions

To check: The validity of the argument p → q q → p ∴ p ↔ q .

Solution Summary: The author explains that the argument lpto q is valid, and the conjunction is false if both the statements are false.

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To check: The validity of the argument p→qq→p ∴p↔q.

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Chapter A Solutions

To check:

The validity of the argument p→qq→p ∴p↔q.