Explanation The form of Disjunctive Syllogism is, Major premise: p ∨ q Minor premise: ∼ p _ Conclusion: q 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 statements are said to be equivalent if the respective truth table of the statement are identical for the corresponding entries. 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 “only if” 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. Given: The given argument is, Disjunctive Syllogism. Approach: The given argument is, Disjunctive Syllogism. The form of Disjunctive Syllogism is, Major premise: p ∨ q Minor premise: ∼ p _ Conclusion: q There are 2 letters in the symbolic expressions. So, there will be 2 2 = 4 rows in the truth table

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ISBN: 9781337349611

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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Chapter 1.6, Problem 2E

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The given argument form is valid.

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The given argument form is valid.

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The given argument form is valid.