# Logical conjunction

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In logic and mathematics, logical conjunction, or: and is a two-place logical connective that has the value true if both of its operands are true, otherwise a value of false.

The analogue of conjunction for a (possibly infinite) family of statements is universal quantification, which is part of predicate logic.

## Contents

### Notation

And is usually expressed with an infix operator. In mathematics and logic, it is usually ; in electronics $\cdot$; and in programming languages, & or and. Some programming languages have a related control structure, the short-circuit and, written &&, and then, etc.

### Definition

Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both of its operands are true.

### Truth table

The truth table of $~A \and B$:

### Introduction and elimination rules

As a rule of inference, conjunction introduction is a classically valid, simple argument form. The argument form has two premises, A and B. Intuitively, it permits the inference of their conjunction.

or in logical operator notation:

Here is an example of an argument that fits the form conjunction introduction:

Conjunction elimination is another classically valid, simple argument form. Intuitively, it permits the inference from any conjunction of either element of that conjunction.

...or alternately,

In logical operator notation: