Eroxl's Notes
Truth Table

A truth table is a mathematical table used in logic to determine the output of a compound statement for every possible combination of input values.

Example

Truth table for the logical statement

F F F F F
F F T F T
F T F F F
F T T F T
T F F F F
T F T F T
T T F T T
T T T T T

Notice how occasionally in-between statements are included to help with computing the final outputs.

Constructing Truth Tables

To construct a truth table the inputs can be written in terms of counting in binary with true representing a 1 and false representing a 0. For example in the previous truth table we start with (FFF), then (FFT), (FTF), , (TFT), (TTT). For truth tables with more or less inputs this process of counting is just repeated until all the inputs are 1's or true.