Definition:Conjunction/General Definition

From ProofWiki
Jump to navigation Jump to search


Let $p_1, p_2, \ldots, p_n$ be statements.

The conjunction of $p_1, p_2, \ldots, p_n$ is defined as:

$\displaystyle \bigwedge_{i \mathop = 1}^n \ p_i = \begin{cases} p_1 & : n = 1 \\ & \\ \displaystyle \left({\bigwedge_{i \mathop = 1}^{n-1} \ p_i}\right) \land p_n & : n > 1 \end{cases}$

That is:

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

In terms of the set $P = \left\{{p_1, \ldots, p_n}\right\}$, this can also be rendered:

$\displaystyle \bigwedge P$

and is referred to as the conjunction of $P$.

Also see