The tutor continues about logic, defining tautology with an example.

In yesterday’s post I began about symbolic logic.

A tautology is a compound statement that is always true. For an example, consider the following two statements:

1. p: Today it will rain.
2. q: Today it won’t rain.

The compound statement p ∨ q, based on the values for p, q, above, is always true. Therefore, in this case, p ∨ q is a tautology. The fundamental reason why is that q is opposite of p: q = ¬ p.

In any case, p will either happen or it won’t; therefore, p ∨ ¬p is a tautology. Generally, for any statement x, x ∨ ¬ x is a tautology.

Source:

Grimaldi, Ralph P. Discrete and Combinatorial Mathematics. Don Mills: Addison-
  Wesley, 1994.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.