JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Truth Tables

Definition : A table that shows the relationship between the truth value of a compound statement \[S(p,q,r,..)\] and the truth values of its sub-statement  \[p,q,r,\text{ }.....\] etc, is called the truth table of statement S.

Construction of truth table : In order to construct the truth table for a compound statement, we first prepare a table consisting of rows and columns. At the top of the initial columns, we write the variables denoting the sub-statements or constituent statements and then we write their truth values, in the last column. We write the truth value of the compound statement on the basis of the truth values of the constituent statements written in the initial columns. If a compound statement is made up of two simple statement, then the number of rows in the truth table will be \[{{2}^{2}}\] and if it is made up of three simple statements, then the number of rows will be \[{{2}^{3}}\]. In general, if the compound statement is made up of n sub-statements, then its truth table will contain \[{{2}^{n}}\] rows.