Definition:Conjunction

Definition
Conjunction is a binary connective written symbolically as $p \land q$ whose behaviour is as follows:


 * $p \land q$

is defined as:
 * $p$ is true and $q$ is true.

This is called the conjunction of $p$ and $q$.

The statements $p$ and $q$ are known as the conjuncts.

$p \land q$ is voiced:
 * $p$ and $q$.

Boolean Interpretation
From the above, we see that the boolean interpretations for $\mathbf A \land \mathbf B$ under the model $\mathcal M$ are:


 * $\left({\mathbf A \land \mathbf B}\right)_{\mathcal M} = \begin{cases}

T & : \mathbf A_{\mathcal M} = T \text{ and } \mathbf B_{\mathcal M} = T \\ F & : \text {otherwise} \end{cases}$

Generalized Notation

 * $\displaystyle \bigwedge_{i \mathop = 1}^n \ p_i = p_1 \land p_2 \land \cdots \land p_{n-1} \land p_n$

Complement
The complement of $\land$ is the NAND operator.

Truth Function
The conjunction connective defines the truth function $f^\land$ as follows:

Notational Variants
Various symbols are encountered that denote the concept of conjunction: