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".

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

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

Boolean Interpretation
From the above, we see that the boolean interpretations for $$p \and q$$ are:

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";
 * $$p$$ & $$q$$.