# Logical AND

Welcome! This is a lesson in the Introductory Discrete Mathematics for Computer Science course here at Wikiversity.

Previous lesson: Using truth tables

I apologize for the name of this lesson. The true name of this operator, which is a diadic operator, is a conjunction. It is a bit dangerous to refer to a conjunction as an AND operator, because English words are far more vague than logic.

• A diadic operator takes 2 arguments, p and q. It returns a single truth value.
• The conjunction, represented by the symbol $\wedge$ , returns the value "true" if and only if both arguments are true.

$\wedge$  : This is the conjunction or AND operator

• Let $p$  represent the statement: It is raining.
Let $q$  represent the statement: I am hungry.
$p\wedge q$  represents the conjunction of statements $p$  and $q$ : It is raining AND I am hungry.

• Let $p$  represent the false statement: It is raining.
Let $q$  represent the true statement: I am hungry.
$p\wedge q$  is false.

## Truth table for conjunction statements

$p\,\!$  $q\,\!$  $p\wedge q$
T T T
T F F
F T F
F F F

## Next lesson

Your next lesson is called Logical OR.