# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.04

## Logic and Set Theory

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Truth Tables
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(figure available in print form)

The truth table for conditional statements is as follows:

(figure available in print form)

What is most confusing about the truth table above is that in only case 2 is the result false. What a conditional statement merely says is that if a hypothesis is true then the conclusion is true. It says nothing of the case where the hypothesis is false, so we arbitrarily give a truth value of true to every case in which the hypothesis is false cases 3 and 4. Thus to define a conditional statement we can say it is always true unless the hypothesis is true and the conclusion is false case 2.

Consider the following example, “If you go to the beach then I’ll never talk to you again.” The hypothesis is “you go to the beach.” If this statement is false that does not necessarily mean that the conclusion is false. I may still talk to you. On the other hand If I do not ever talk to you again it is impossible for you to have gone to the beach.