All highly successful salespersons are both well organized and self-motivated, characteristics absent from many sales...

ElliottF July 17, 2020

Question

I initially diagrammed the first conditional here as: HSSP -> WO & SM When I wrote the contrapositive I wrote it as: ~WO or ~SM -> ~HSSP In the answer explanation it has this written as: ~HSSP -> ~WO or ~SM This seems to be just negating and switching the and to or. Did I remember something from this lesson incorrectly? I arrived at the correct answer to this anyway as I was able to eliminate the other choices, but I want to be sure I’m clear on how to diagram contrapositives of statements like the one above. Thanks!

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shunhe July 17, 2020

Hi @ElliottF,

Thanks for the question! Don’t worry, the way you diagrammed the first conditional and the contrapositive are correct. Taking the contrapositive of

A —> B

is just

~B —> ~A

And when “A” is a compound statement, like (X & Y), then we have to negate that conditional. And the negation of (X & Y) is (~X v ~Y), and the negation of (X v Y) is (~X & ~Y). In other words, we negate both variables individually, and switch the & to an v, or an v to an &. So your diagram was right.

What the answer choice was diagramming was the next part, where we’re told that those are “characteristics absent from many salespersons who are not highly successful.” So they wrote out “Many not Highly successful are not Well organized OR not self motivated” to represent that statement. Which is a bit odd, but a perfectly fine thing to do.

Hope this helps! Feel free to ask any other questions that you might have.