Difference between revisions of "Negation of implies"
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==Statement== | ==Statement== | ||
Here is the [[truth table]] for [[implies]], with the negation computed (the negation is simply {{M|\neg(A\implies B)}} - so {{M|\neg}} of whatever is in the {{M|A\implies B}} column) | Here is the [[truth table]] for [[implies]], with the negation computed (the negation is simply {{M|\neg(A\implies B)}} - so {{M|\neg}} of whatever is in the {{M|A\implies B}} column) | ||
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! {{M|B}} | ! {{M|B}} | ||
! {{M|A\implies B}} | ! {{M|A\implies B}} | ||
| + | ! style="min-width:3em;" | | ||
| + | ! {{M|A}} | ||
| + | ! {{M|\neg B}} | ||
| + | ! {{M|A\wedge(\neg B)}} | ||
! {{M|\neg(A\implies B)}} | ! {{M|\neg(A\implies B)}} | ||
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Latest revision as of 21:05, 17 November 2016
Stub grade: C
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Formal logic pages to not exist!
Grade: C
This page requires cleaning up
Some aspect of this page is rather messy and it needs to be cleaned up
The message provided is:
Warning:That grade doesn't exist!
The message provided is:
A low grade as the content is and the page isn't important
Warning:That grade doesn't exist!
Statement
Here is the truth table for implies, with the negation computed (the negation is simply [ilmath]\neg(A\implies B)[/ilmath] - so [ilmath]\neg[/ilmath] of whatever is in the [ilmath]A\implies B[/ilmath] column)
| [ilmath]A[/ilmath] | [ilmath]B[/ilmath] | [ilmath]A\implies B[/ilmath] | [ilmath]A[/ilmath] | [ilmath]\neg B[/ilmath] | [ilmath]A\wedge(\neg B)[/ilmath] | [ilmath]\neg(A\implies B)[/ilmath] | |
|---|---|---|---|---|---|---|---|
| T | T | ||||||
| T | T | ||||||
| T | T | T | T | T | |||
| T | T | T | T |
It is easy to see that the negation of implies is the same as [ilmath]A\wedge(\neg B)[/ilmath]
So to negate [ilmath]A\implies B[/ilmath] we require to have [ilmath]A[/ilmath] but not [ilmath]B[/ilmath]
