College Math

College Math Study Guide

6.9 Converse, Inverse, and Contrapositive Let us take each of these one by one, and explain them using examples. For instance, If it is Sunday, then it will rain. In this case, the antecedent is “it is Sunday” = a And, the consequent is “it will rain” = b The above mentioned conditional statement can be written as a → b The converse of the statement will be when we interchange the antecedent with the consequent, that is: b → a It can be written as, “If it will rain, then it is Sunday” The inverse of the statement is found when we negate both the antecedent as well as the consequent, that is: (~a) → ~b It can be written as, “If it is not Sunday, it will not rain”. The con r positive statement is obtained when we interchange the antecedent with the consequent, and also negate both of them. (~b) → ~a It can be written as, “If it will not rain, then it is not Sunday”. 6.10 Logical Arguments A logical argument is a list of assumptions, rules, observations or facts, known as premises , after which a single statement ( conclusion ) can be drawn. Example 1: Premise 1: All roses are red. Premise 2: I have one rose. Conclusion: Therefore, my rose is red. Example: 2: Premise 1: All rabbits eat carrots. Premise 2: I have a pet rabbit. Conclusion: Therefore, my rabbit eats carrots.

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