Tautologies and ContradictionTautologiesA 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.
Next TopicPredicate Logic
