Tautologies and Contradiction

Tautologies

A proposition p is a tautology when it is true in all situations. P tautology contains only the True in the field of the column of its truth table.

Example: (p⟶q) ↔(∼q⟶∼p) is a tautology

pqp⟶q~p~q~q⟶~p(p⟶q) ↔(∼q⟶∼p)
TTTFFTT
TFFFTFT
FTTTFTT
FFTTTTT

So the (p⟶q) ↔(∼q⟶∼p) is containing True in all of its rows.

Contradiction

In Contradiction, a statement is always false. It is the opposite of Tautology.

Example: p ∧∼p is a contradiction

p~pp^~p
TFF
FTF

Here in p^~p all statements are false, so it will be a contradiction.

Contingency

A statement can either be True or False depending on the truth values of its variables is called a contingency. It is neither tautology nor contradiction.

pqp⟶qp∧q(p⟶q) ⟶ (p∧q)
TTTTT
TFFFT
FTTFF
FFTFF

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