The result is as follows:

Definition 3 (Tautology). A tautology is a proposition that is always true for any of its variables.

Definition 4 (Contradiction). A contradiction is a proposition that is always false for any value of its variables.

Theorem 4.4. If proposition P is a tautology then ~P is a contradiction, and conversely.

Proof. If P is a tautology, then all elements of its truth table are false (by Definition 1), so all elements of the truth table for ~P are false, therefore ~P is a contradiction (by Definition 2). ⬜

Example 2. "It is raining or it is not raining" is a tautology, but "it is not raining and it is raining" is a contradiction.

Remark 2. Example 1 used De Morgan's Law ~(pq) ≡ ~p ∧ ~q.