Math & Comp Sci: Symbolic Logic: another tautology

The tutor follows up about tautology with another example.

For grounding about the symbols, etc, readers may want to refer to my Feb 12 post.

In my Feb 13 post I defined tautology with a simple example. Today, I’ll give a more involved one.

A tautology is a compound statement which is always true. Consider the following example:

(¬p ∨ q) ⊻ (p ∧ ¬q)

The central sign ⊻ is exclusive or; it’s true if one of the inputs is, but not both.

Let’s imagine both p, q false (0). Then the first bracket is true, the second false, so the entire statement is true.

If p is true, q false, then first bracket is false, but the second bracket is true. Once again, the full statement is true.

If q is true, then the first bracket is true, the second false: the full statement is true.

Source:

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

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

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