Disjunction OR

Disjunction OR

In logic, a disjunction is a compound sentence formed by combining two sentences (or facts) using the word “or.”
A disjunction is true when EITHER or BOTH sentences (or facts) are true.

Examples:

1. “Blue is a color or 7 + 3 = 10.”
   (T or T = T) Since both facts are true, the entire sentence is true.
2. “One hour = exactly 55 minutes or one minute = exactly 60 seconds.”
   (F or T = T) Since the second fact is true, the entire sentence is true.
3. “3 + 4 = 6 or all dogs meow.”
   (F or F = F) Since both facts are false, the entire sentence is false.
4. “The word cat has 3 letters or the word dog has four letters.”
   (T or F = T) Since the first fact is true, the entire sentence is true.

Mathematicians often use symbols and tables to represent concepts in logic. The use of these variables, symbols and tables creates a shorthand method for discussing logical sentences.

A truth table is a pictorial representation of all of the possible outcomes of the truth value of a compound sentence. Letters such as p and q are used to represent the facts (or sentences) within the compound sentence.

Truth table for disjunction (or):
(notice the symbol used for “or” in the table below)

Remember:
For a disjunction (or) to be true, EITHER or BOTH facts must be true.

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