The tutor lays a foundation for posts about symbolic logic.

In logic, shorthand such as p→q is used; it means “p implies q.” p ∨ q means “p or q.” p ∧ q means “p and q”. ¬p means “not p”. p, q would each stand for a statement such as “It’s raining” or “The date is Feb 12”.

p→q can be true or false depending on the values of p and q. If they are both false, for instance, p→q is true, since q is in the same state as p. If p is false but q is true, p→q is true. Perhaps surprising, the reasoning for this case is that q is true regardless of p; whatever p is, it implies q. If p is true but q is false, p→q is false, because p’s being true fails to make q also true. Lastly, and intuitively, if both are true then p→q is true. Often, 0 is used for false, 1 for true.

A compound statement is two or more statements linked by one or more “ands” or “ors”. Therefore, p ∨ q is a compound statement. To return to the possible values for p, q, proposed in the first paragraph, we have

p ∨ q means “It’s raining or the date is Feb 12.”

Regardless of the meanings of p, q, in a given case, p ∨ q is true when one or both are true; p ∧ q is true only when both p, q, are true.

⊻ means “exclusive or”. p ⊻ q is true when exactly one of p, q, is true (not both).

I’ll be talking more about logic in future posts:)

Source:

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

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