Explain Tautologies, contradiction and contingencies with suitable examples.

Tautology: A compound proposition is said to be a tautology if it is always true no matter what the truth values of the atomic proposition that contain in it.

E.g.: p→q↔¬p∨q

p	Q	¬p	p→q	¬p∨q	p→q↔¬p∨q
T	T	F	T	T	T
T	F	F	F	F	T
F	T	T	T	T	T
F	F	T	T	T	T

Since the truth values of p→q↔¬p∨q is always true for all the possible cases : p→q↔¬p∨q is a tautology.

Contradiction:  A compound proposition is said to be contradiction if it is always false no matter what the truth values of the atomic proposition that contain in it.

Eg: p ˄¬p

p	¬p	p ˄ ¬p
T	F	F
F	T	F

Since the truth values of p ˄¬p is always false for all the possible cases p ˄¬p is a contradiction.

Contingencies: A compound proposition that is neither tautology nor contradiction is called contingency.

Eg: p ˄ q

p	Q	p ˄ q
T	T	T
T	F	F
F	T	F
F	F	F

Since the truth values of p ˄q is neither all true nor all false so it is a contingency.