\begin{definition}[Definition:Conjunction/General Definition]
Let $p_1, p_2, \ldots, p_n$ be statements.
The '''conjunction''' of $p_1, p_2, \ldots, p_n$ is defined as:
:$\ds \bigwedge_{i \mathop = 1}^n \ p_i = \begin {cases}
p_1 & : n = 1 \\
& \\
\ds \paren {\bigwedge_{i \mathop = 1}^{n - 1} p_i} \land p_n & : n > 1
\end {cases}$
That is:
:$\ds \bigwedge_{i \mathop = 1}^n \ p_i = p_1 \land p_2 \land \cdots \land p_{n - 1} \land p_n$
In terms of the set $P = \set {p_1, \ldots, p_n}$, this can also be rendered:
:$\ds \bigwedge P$
and is referred to as the '''conjunction of $P$'''.
\end{definition}