A truth table is a table in which the truth or falsity of a statement is listed for all possible proposition conditions. A truth able lists the value of the dependent variable for each set of values of the independent variables. Suppose there are three variables C, A and B, wherein the variable C is being derived from some expression based on the variables A and B.
Then, C is called the dependent variable because i is dependent on and being derived from A and B. Variables A and B are independent variables because they do not depend on any thing. So, in this example, preparing a truth table means deriving the value for dependent variable i.e. C for each set of values of independent variables (A and B).
Bu in Boolean algebra any variable can have only two values i.e. 0 and 1.
So A and B can only have values 0 and 1.
together they can have 4 possible combinations of 0 and 1 as follows.
Table 1 : Possible values of A and B
Calculating the value for C for each possible set of values of A and B is called the Truth Table.
Table 2 : Truth able for values of A, B, and C
A B C
0 0 0
0 1 0
1 0 0
1 1 1