Truth Tables

Truth tables are a way to visualize all the possible solutions to any logical argument. Truth tables can be used to write out all the possible combinations of a given number of variables. So if we have 2 variables, A and B then the truth table would be:

Remembering the previous example of “If it is raining then I wear my raincoat” where

A = It Is raining

B = I wear my raincoat

The meaning column would usually not be in the table and is put there so you understand what each line means.

TT it is raining and I’m wearing my raincoat
TFit is raining and I am not wearing my raincoat
FT it is not raining and I am wearing my raincoat
FFit is not raining and I am not wearing my raincoat

Now these are all the POSSIBLE solutions but these are not all logical truths. This will make more sense in the following pages as we go over the operators and start adding columns to our truth tables.

Whenever you have a logic problem involving 2 variables the first step you should do is draw the first 2 columns of the above table. As we go through the logical operations we will be using truth tables to express how you can visualize arguments. If you can master truth tables then you will have no problem figuring out all the logic problems on the CLEP math exam.

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