# Logical AND

 Type classification: this is a lesson resource.

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

${\displaystyle \wedge }$  : This is the conjunction or AND operator

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

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

## Truth table for conjunction statements

${\displaystyle p\,\!}$  ${\displaystyle q\,\!}$  ${\displaystyle p\wedge q}$
T T T
T F F
F T F
F F F

## Next lesson

Your next lesson is called Logical OR.