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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].

<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].

'''Logical equality''' is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both operands are false or both operands are true.

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

The [[truth table]] of '''p EQ q''' (also written as '''p = q''', '''p &harr; q''', or '''p &equiv; q''') is as follows:

The [[truth table]] of <math>p ~\operatorname{EQ}~ q,</math> also written as <math>p = q,\!</math> <math>p \Leftrightarrow q,\!</math> or <math>p \equiv q,\!</math> is as follows:

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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"

{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"

|+ '''Logical Equality'''

|+ style="height:30px" | <math>\text{Logical Equality}\!</math>

|- style="background:#e6e6ff"

|- style="height:40px; background:#f0f0ff"

! style="width:15%" | p

| style="width:33%" | <math>p\!</math>

! style="width:15%" | q

| style="width:33%" | <math>q\!</math>

! style="width:15%" | p = q

| style="width:33%" | <math>p = q\!</math>

|-

|-

| F || F || T

| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>

|-

|-

| F || T || F

| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>

|-

|-

| T || F || F

| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>

|-

|-

| T || T || T

| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>

|}

|}