What Are the Related Conditionals: Converse, Inverse, and Contra-positive? Compound statements that contain related conditionals can be of three types: converse, inverse, and contra-positive. Converse - For two statements A and B, the converse of the implication A implies B is the statement: A implies B. The converse of A implies B is more commonly written as: If A, then B. The implication and the converse take up different truth values when there is one simple statement (either A or B) is true, and the other statement is false. Inverse - For two statements A and B, the inverse of the implication A implies B is the statement (not A) implies (not B). The inverse of A implies B is more commonly written as: If not A, then not B. Contrapositive - For two statements A and B, the contrapositive of the implication A implies B is the statement: (not A) implies (not B). The contrapositive of A implies B is more commonly written as: If not A, then not B.

When we evaluating conditional statements we will often be asked to modify the relationship between the hypothesis and the conclusion. In some cases this can change the total truth value of the conditional. There are usually three ways in which we move these around. We can switch the position of the hypothesis and conclusion this is called a converse. We can also negate the statement by taking the inverse of both the hypothesis and conclusion. We can also negate the converse which is called the contrapositive. Your students will use the following activity sheets to learn how to rewrite statements according to related conditionals, including converse, inverse, and contra-positive conditionals. Please note that student answers may vary slightly.