A truth table is a way of representing the logical values of an expression made up of variables and operators. A tautology is a logical statement that is always true. To complete the truth table for the statement (a∧∼b)∧(a⇒b), you will need to list out all possible combinations of the logical values for a and b, then determine the result for each combination.
The truth table for (a∧∼b)∧(a⇒b) is as follows:
Based on the results in the truth table, the statement (a∧∼b)∧(a⇒b) is a tautology. This is because the statement is true for all combinations of the logical values for a and b.