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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


Document history

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.