Explanation Given: The given statements are, If handguns are outlawed, then outlaws have handguns. If outlaws have handguns, then handguns are outlawed. Approach: 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 statements are, If handguns are outlawed, then outlaws have handguns. If outlaws have handguns, then handguns are outlawed. Let, p : Handguns are outlawed, and q : Outlaws have handguns. Now, the given statements can be written as, p → q : If handguns are outlawed, then outlaws have handguns. q → p : If outlaws have handguns, then handguns are outlawed. There are 2 letters in the given symbolic expression

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ISBN: 8220100546112

Author: MOWRY

Publisher: Cengage Learning US

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Chapter 1.3, Problem 45E

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Each pair of statements are equivalent by truth table.

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Chapter 1.3, Problem 44E

Chapter 1.3, Problem 46E

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To check: Each pair of statements are equivalent by truth table.

Solution Summary: The author explains how the truth table shows that the two statements are not equivalent.

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Each pair of statements are equivalent by truth table.