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 $$q$$".

The symbol $$\and$$ is also known as "wedge".

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
Alternative symbols that mean the same thing as $$p \and q$$ are also encountered:


 * $$p\ \texttt{AND}\ q$$;
 * $$p.q$$, referred to as "dot";
 * $$p$$ & $$q$$.