Equivalent Statements · Example 3

Use the conditional statement, “If all dogs bark, then Lassie likes to bark,” to identify the following.

(a) Write the hypothesis of the conditional statement and label it with a $p$.
(b) Write the conclusion of the conditional statement and label it with a $q$.
(c) Identify the following statement as the converse, inverse, or contrapositive: “If Lassie likes to bark, then all dogs bark.”
(d) Identify the following statement as the converse, inverse, or contrapositive: “If Lassie does not like to bark, then some dogs do not bark.”
(e) Which statement is logically equivalent to the conditional statement?

OpenStax, Contemporary Mathematics · §2.5 Equivalent Statements · Example 3