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==Logical NAND==

==Logical NAND==

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 propositions, 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 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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{| 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 &uarr; 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>

|}

|}