# Logical AND

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Previous lesson: Using truth tables

## Your first diadic operator!

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 [math]\wedge[/math], returns the value "true" if and only if both arguments are true.

[math]\wedge[/math] : This is the conjunction or AND operator

- Let [math]p[/math] represent the statement: It is raining.

- Let [math]q[/math] represent the statement: I am hungry.
- [math]p \wedge q[/math] represents the
**conjunction**of statements [math]p[/math] and [math]q[/math]: It is raining AND I am hungry.

- [math]p \wedge q[/math] represents the

- Let [math]q[/math] represent the statement: I am hungry.

- Let [math]p[/math] represent the false statement: It is raining.

- Let [math]q[/math] represent the true statement: I am hungry.
- [math]p \wedge q[/math] is false.

- Let [math]q[/math] represent the true statement: I am hungry.

## Truth table for conjunction statements

[math]p \,\![/math] | [math]q \,\![/math] | [math]p \wedge q[/math] |
---|---|---|

T | T | T |

T | F | F |

F | T | F |

F | F | F |

## Next lesson

Your next lesson is called Logical OR.