### Conjunction

Definition:

- Two propositions connected by 'and'.

Example:

- "Four is even and three is odd."

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

- E = "Four is even."
- O = "Three is odd."

And replacing 'and' with the symbol for conjunction: '&' The above conjunction can be symbolized thus:

- E & O

The components to the right and left of 'and' are called conjuncts. It can readily seen that a conjunction is true only when both conjuncts are true. For the proposition, "Four is even and three is odd.", to be true, it must be the case that four is even and it must be the case that three is odd. So the truth value of the conjunction is a function of the truth value of its components. If one or both of the components are false, then the conjunction is false. In logic this characterized by a truth table:

CONJUNCTION

INPUT | OUTPUT
--- | ---
E......O | E & O
T......T | T
T......F | F
F......T | F
F......F | F

Examples of conjunction:
(~N . ~M)
[(G > V) . X]
[(H + F) > D] . [B > (U > Z)]