The Coffee Shoppe can avoid a decrease in overall profitability only if its coffee sales do not decrease.

MelodyWilson September 18, 2020

Why not A?

Hi team. I selected answer choice A as my answer because I thought the contrapositive of not CS decrease-> not OP decrease was the answer. Could someone explain why A isn’t the answer please? I get stomped on this question every-time.

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shunhe September 18, 2020

Hi @MelodyWilson,

Thanks for the question! So we’re told that the coffee shoppe can avoid a decrease in overall profitability only if its coffee sales do not decrease. Remember that “only if” introduces the necessary condition; we diagram X only if Y as X —> Y. So how do we diagram this? Well, avoiding a decrease in overall probability is the same as saying there is NOT a decrease in overall profitability. So we can diagram this

~Decrease in overall profitability —> ~Coffee sales decrease

And what’s the contrapositive of this? It’s that

Coffee sales decrease —> Decrease in overall profitability

So we can see that the original conditional matches with answer choice (E). (A), on the other hand, is a mistaken negation. You might have diagrammed the “only if” as introducing the sufficient condition.

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

MelodyWilson September 18, 2020

Thank you! It does. I need to review those S &N notecards again lol.