Negation of implies

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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]\neg(A\implies B)[/ilmath]
		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]