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

The truth table of ${\displaystyle p~\operatorname {EQ} ~q,}$ also written ${\displaystyle p=q,\!}$ ${\displaystyle p\Leftrightarrow q,\!}$ or ${\displaystyle p\equiv q,\!}$ appears below:

${\displaystyle {\text{Logical Equality}}\!}$

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

Syllabus

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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.

• Logical Equality, InterSciWiki
• Logical Equality, Wikinfo
• Logical Equality, Wikiversity
• Logical Equality, Wikiversity Beta
• Logical Equality, Wikipedia