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new here (apologies for the formatting). I want to express the relationship between $$A \longrightarrow B$$ and $$B \longrightarrow \neg A.$$

Clearly this is neither converse, inverse, nor contrapositive; does it have a name at all?

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    If the first one implies the second one, you get a contradiction ($A \rightarrow \neg A$). Same the other way around since the second statement is equivalent to $A \rightarrow \neg B$ which means that $A$ implies both $B$ and $\neg B$. In all, I don't know if there is a specific name for this.2011-04-04
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    I'm not sure you have the notation right in your title - the converse of the inverse (or inverse of the converse) is the contrapositive $\neg B \longrightarrow \neg A$.2011-04-04
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    @Cheezmeister: What is the "contradiction" of a proposition? If you mean the negation, then note that the negation of the converse of $A\rightarrow B$ is $\neg(B\rightarrow A) = B\land \neg A$, which is not $B\rightarrow \neg A$.2011-04-04
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    B->-A gives the same truth values as -(A and B)2011-04-04
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    @David These are independent statements that I'm simply comparing. @Michael Right you are, sir. I've fixed the title.2011-04-04
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    @Cheezmeister: Essentially, you want to from $\neg A\lor B$ to $\neg A\lor \neg B$; so perhaps that's a better description: negating one term in a disjunction.2011-04-04
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    @Arturo I'm using the terms [here](http://en.wikipedia.org/wiki/Contrapositive#Comparisons). I'll admit I'm rather rusty :)2011-04-04
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    @Cheezmeister: Fair enough.2011-04-04

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