Truth table is a method of showing logical relationships between statements. Truth tables are used by logicians, computer engineers, and others who reason by symbolic logic.
To understand truth tables, we must first understand some ideas of logic. A basic declarative sentence is a proposition if it can be classified as true or false. For example, the sentences The door is open. and The light is on. are propositions.
When propositions are combined using such logical connectives as and, or, or if … then … , they form propositional functions. For example, the two propositions above may be combined into the propositional function The door is open, and the light is on. The truth or falsity of a propositional function depends on the truth or falsity of each of the basic propositions and the way the function relates to them.
The truth table corresponding to the above propositional function would look like this:
The table begins with a list of all combinations of true and false values that can be assigned to the basic propositions. The table is completed by indicating the truth or falsity of the propositional function for each combination.
