Logical equality

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

${\text{Logical Equality}}\!$
$p\!$	$q\!$	$p=q\!$
$\operatorname {F}$	$\operatorname {F}$	$\operatorname {T}$
$\operatorname {F}$	$\operatorname {T}$	$\operatorname {F}$
$\operatorname {T}$	$\operatorname {F}$	$\operatorname {F}$
$\operatorname {T}$	$\operatorname {T}$	$\operatorname {T}$

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