### Disjunction

Definition:

- Two propositions connected by 'or'.

Example:

- "Either I'll give you a penny or I'll give you a quarter."

Following the logical convention of having a single letter represent a proposition:

- P = "I'll give you a penny."
- Q = "I'll give you a quarter."

And replacing either...or...' with a symbol for disjunction: in this case '+'. The above disjunction can be symbolized thus:

- P + Q

The components to the right and left of 'or' are called disjuncts. A disjunction is false only when both disjuncts are false. In every other case it is true. The disjunction "Either I'll give you a penny or I'll give you a quarter." is false only if it is false that I give you a penny and it is false that I give you a quarter. In every other case it is true. It is true if I only give you a penny. It is true if I only give you a quarter. And it is true if I give you both a penny and a quarter. The truth value of a disjunction is a function of the truth value of its disjuncts. In logic this characterized by a truth table:

DISJUNCTION

INPUT | OUTPUT
--- | ---
P......Q | P + Q
T......T | T
T......F | T
F......T | T
F......F | F

Examples of disjunctions:
(A + B)
[(F > ~P) + K]
[(~L K) . N] + [(D . G) > X]