TautologyQ

TautologyQ[bf] gives True if all combinations of values of variables make the Boolean function bf yield True.

TautologyQ[expr, {a1, a2, ...}] gives True if all combinations of values of the ai make the Boolean expression expr yield True.

Examples

Check for tautology:

TautologyQ[a || !a]
(* True *)

Non-tautology:

TautologyQ[a && b]
(* False *)

Please visit the official Wolfram Language Reference for more details.