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, 14:26, 15 May 2012
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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]]. |
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− | The '''logical NAND''' is a [[logical 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 true. In other words, it produces a value of ''true'' if and only if at least one of its operands is false. | + | The '''logical NAND''' 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 true. In other words, it produces a value of ''true'' if and only if at least one of its operands is false. |
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− | The [[truth table]] of '''p NAND q''' (also written as '''p | q''' or '''p ↑ q''') is as follows: | + | The [[truth table]] of <math>p ~\operatorname{NAND}~ q,</math> also written <math>p \stackrel{\circ}{\curlywedge} q\!</math> or <math>p \barwedge q\!</math> appears below: |
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| <br> | | <br> |
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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 NAND''' | + | |+ style="height:30px" | <math>\text{Logical NAND}\!</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 \stackrel{\circ}{\curlywedge} q\!</math> |
| |- | | |- |
− | | F || F || T | + | | <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</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 || F | + | | <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math> |
| |} | | |} |
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