Sufficient & Necessary Questions - - Question 2

"If the forest continues to disappear at its present pace, the koala will approach extinction," said the biologist. "...

HannahNg February 2, 2020

Sufficient and Necessary Part

So I understand the logic to conclude why B is the correct answer. But I'm still wondering the process to decide the S and N part. The politician said "So all that is needed...deforestation". How can we decide "stop deforestation" is the S part? And the answer choice, in both the first two answer choices, we have the same structure like: A and B (FCD AND KAE), does that AND establish double arrow? Like we can say either FCD and KAE or KAE and FCD? Thanks!

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SamA February 4, 2020

Hello @HannahNg,

This is a tricky one, and a good way to test your sufficient and necessary understanding.

Biologist: FCD - - - - - - - - > KAE
contrapositive: not KAE - - - - - - -> not FCD

Remember that "all" introduces the sufficient condition.

Politician: not FCD - - - - - - -> not KAE
contrapositive: KAE - - - - - - -> FCD

In other words, the biologist believes that stopping deforestation is necessary for saving the koalas, while the politician believes that stopping deforestation will guarantee koala survival.

The answer choices are not establishing a double arrow. Rather, they present two events, and we have to decide if they could both occur, according to the biologist and the politician. We want to take the given conditions, and plug them into the "formulas" presented by these people.

A. Deforestation continues and the koala becomes extinct (FCD and KAE). Does it conflict with the necessary condition of either the scientist or the biologist? No.

B. Deforestation is stopped and the koala becomes extinct (not FCD and KAE). This does not contradict the biologist.

What about the politician? The politician clearly states what will happen when deforestation is stopped. The koalas will be saved (not KAE).

not FCD - - - - - - - - - > not KAE

This is why scenario given in answer choice B is not possible. It directly contradicts the necessary condition given by the politician.

Does that answer your question?

pat4uclalaw February 25, 2020

Hello,
So if "All" introduces a sufficient condition, and the politician says "So all that is needed to save the Koala is to stop deforestation."

So why can't we write:

not KAE-----> not FCD

The "all that is needed to save the koala" comes first so wouldn't that be the sufficient?

Thank you!

AndreaK March 15, 2020

Hi @pat4uclalaw,

I think this use of language is best interpreted intuitively. Remember a sufficient condition guarantees an outcome. A necessary condition is required for an outcome to come to pass, but does not guarantee that outcome will come to pass.

"All that is needed to save the koala is to stop deforestation."

In other words, this is saying that THE ONLY (sufficient condition indicator phrase) thing we need to save the koala is to stop deforestation. Stoping deforestation in and of itself would be sufficient to save the koala species, because it is THE ONLY thing that is needed (all that is needed) to do so. In other words, logically this sentence means you could save the koala just by stopping deforestation. You would never need to do anything else to save the species. That's why it's sufficient. "All that is needed..." is referring to stopping deforestation (needing to stop deforestation to save it). It wouldn't make sense for that sentence to mean all that is needed is to save the koala is to save the koala. It's saying instead that all that is needed is to stop deforestation, in order to save the koala.

So, not FCD (stopping deforestation) - -> not KAE (koala is saved).
KAE (we don't save the koala) - -> FCD (we didn't stop deforestation).

What you wrote above is actually the statement the biologist is making!

Save the koala - - > stopped deforestation
Deforestation - - > not saving the koala

Hope this helps!

Valentina July 19, 2020

If "the only" is a sufficient condition indicator phrase, why wouldn't the sufficient condition be not KAE? In your sentence, "the only thing we need to do to save the koala...," "the only" precedes "save the koala" aka not KAE

shunhe July 23, 2020

Hi @Valentina,

Thanks for the question! So actually, let’s look at that sentence again. The only thing we need to save the koala is to stop deforestation. What follows “the only”? It’s not “save the koala.” It’s “thing we need to do.” And what is that “thing we need to do”? Well, it’s to stop deforestation! So this could be diagrammed

Thing we need —> ~KAE

But we know that the thing we need to do is to stop deforestation, so instead we can just write

~Deforestation —> ~KAE

which makes sense, since if the only thing we need to save the koala is to stop deforestation, then that implies that if we stop deforestation, we’ll save the koala (since that’s the only thing we needed to do).

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