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:

$\ds \bigwedge_{i \mathop = 1}^n \ p_i = \begin {cases} p_1 & \text{if } n = 1 \\ & \\ \ds \paren {\bigwedge_{i \mathop = 1}^{n - 1} p_i} \land p_n & \text{if } n > 1 \end {cases}$

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 $P$.

Also see