Tautology, Contradiction, and Contingency in Propositional Logic | Discrete Mathematics

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Tautology, Contradiction & Contingency, Discrete Mathematics, GATE, LECTURE, cse, it, mca, Tautology, Identically true formula, Logical truth, Universally valid formula, Contradiction, Identically false, Logical false, Contingency, Contingent formula, Disjunction and Conjunction of Tautologies, Contradictions, and Contingencies, tautology contradiction contingency exercises,
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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∨q 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.