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<font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
<font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
'''Logical conjunction''' 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 of its operands are true.
'''Logical conjunction''' 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 of its operands are true.
The [[truth table]] of '''p AND q''' (also written as '''p ∧ q''', '''p & q''', or '''p<math>\cdot</math>q''') is as follows:
The [[truth table]] of <math>p ~\operatorname{AND}~ q</math> (also written as <math>p \land q\!</math> or <math>p \cdot 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 Conjunction'''
|+ style="height:30px" | <math>\text{Logical Conjunction}\!</math>
|- style="background:#e6e6ff"
|- style="height:40px; background:#f0f0ff"
| style="width:33%" | <math>p\!</math>
| style="width:33%" | <math>q\!</math>
| style="width:33%" | <math>p \land q</math>
|-
|-
| F || F || F
| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</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>
|}
|}