### Tautologies :-

Compound propositions that are always true irrespective of the truth values of the individual simple propositions are called tautologies.

For example, if A_{1} = 2 | A_{2} = 3 | A_{3} = 5

then the compound proposition “A_{i} is not divisible by 6″ is a tautology.

Some common tautologies defined on universe of discourse X are as follow: