Definition:Conjunction

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


 * $$p \and q$$

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.

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

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


 * $$\left({\mathbf A \and \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}$$

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

Truth Table
The truth table of $$p \and q$$ and its complement is as follows:

$$\begin{array}{|cc||c|c|} \hline p & q & p \and q & p \uparrow q \\ \hline F&F&F&T\\ F&T&F&T\\ T&F&F&T\\ T&T&T&F\\ \hline \end{array}$$

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