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Logical conjunction

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Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both of its operands are true.

A logical conjunction of propositions and may be written in various ways.  Among the most common are these:

A truth table for appears below:


A logical graph for is drawn as two letters attached to a root node:

Logical Graph PQ.jpg

Written as a string, this is just the concatenation   The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means

A Venn diagram for indicates the region where is true by means of a distinctive color or shading.  In this case the region is a single cell, as shown below:

Venn Diagram P ∧ Q 2.0.jpg

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Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.