Tautologies and Contradiction

Tautologies

A proposition P is a tautology if it is true under all circumstances. It means it contains the only T in the final column of its truth table.

Example: Prove that the statement (p⟶q) ↔(∼q⟶∼p) is a tautology.

Solution: Make the truth table of the above statement:

As the final column contains all T's, so it is a tautology.

Contradiction:

A statement that is always false is known as a contradiction.

Example: Show that the statement p ∧∼p is a contradiction.

Solution:

Since, the last column contains all F's, so it's a contradiction.

Contingency:

A statement that can be either true or false depending on the truth values of its variables is called a contingency.