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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 disjunction''', also called '''logical alternation''', is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if both of its operands are false.

'''Logical disjunction''', also called '''logical alternation''', is an operation on two logical values, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if both of its operands are false.

The [[truth table]] of '''p OR q''' (also written as '''p &or; q''') is as follows:

The [[truth table]] of <math>p ~\operatorname{OR}~ q</math> (also written as <math>p \lor 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 Disjunction'''

|+ style="height:30px" | <math>\text{Logical Disjunction}\!</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 &or; q

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

|-

|-

| F || F || F

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

|-

|-

| F || T || T

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

|-

|-

| T || F || T

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

|-

|-

| T || T || T

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

|}

|}