A compound proposition that is always true, no matter what the truth values of the atomic propositions that contain in it, is called a tautology.
For e.g. p ∨ ¬p is always true.
A compound proposition that is always false is called contradiction.
For e.g. p ∧ ¬p is always false.
A compound proposition that is neither a tautology nor a contradiction is called a contingency.
For e.g. ¬p ∧ ¬q is true/false both.
Example − Prove [(A → B) ∧ A] → B is a tautology.
Example − Prove (A ∨ B) ∧ [(￢A) ∧ (￢B)] is a contradiction.
Example − Prove (A ∨ B) ∧ (￢A) is a contingency.
