# Logical conjunction

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.

The truth table of ${\displaystyle p~\operatorname {AND} ~q,}$ also written ${\displaystyle p\land q\!}$ or ${\displaystyle p\cdot q,\!}$ appears below:

 ${\displaystyle p\!}$ ${\displaystyle q\!}$ ${\displaystyle p\land q}$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {T} }$

## 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.