#5 - Astronaut: Any moon, by definition, orbits some planet

[Administrator]

Complete Question Explanation

Justify the Conclusion-SN. The correct answer choice is (C)

The astronaut says that every moon necessarily orbits a planet in a solar system; the astronaut concludes that every moon in solar system S4 orbits the planet Alpha. There is one missing assumption which would make this argument completely air-tight: we need to establish that Alpha is the only planet in S4. If there are multiple planets in S4, the moons could be orbiting planets other than Alpha.

Note that the question stem is looking for a single answer choice which, by itself, will fully logically complete the argument. The question stem is looking for an answer choice which is sufficient (but maybe not necessary).

Answer choice (A): This answer choice does not complete the argument. We could have only one moon in S4, but perhaps it orbits a different planet, Beta.

Answer choice (B): This answer choice does not complete the argument. Consider the following story: we have two moons in S4, Moon I and Moon II. We have two planets in S4, Alpha and Beta. Moon I orbits Beta and Moon II orbits Beta. This story is perfectly consistent with the premises of the stimulus and with the statement of answer choice (B), but it fails to prove the author's conclusion.

Answer choice (C): This is the correct answer choice. If the statement in this answer choice is true, then it must be that every moon in S4 orbits Alpha (the only possible planet in the solar system).

Answer choice (D): This answer choice does not complete the argument. Imagine we have four moons (I, II, III, and IV) and two planets (Alpha and Beta). Alpha is orbited by Moon I and Moon II; Beta is orbited by Moon III and Moon IV. This story is perfectly consistent with the premises of the stimulus and with the statement of answer choice (D), but it fails to prove the author's conclusion.

Answer choice (E): This answer choice does not complete the argument. Imagine we have two moons (I and II) and two planets (Alpha and Beta). Imagine that Alpha is orbited by Moon I and Beta is orbited by Moon II. This story is perfectly consistent with the premises of the stimulus and with the statement of answer choice (E), but it fails to prove the author's conclusion.

[Basia W]

Good afternoon,

I have a question regarding question 10 in Lesson 4 HW. The answer key says that "every moon necessarily orbits a planet in the system" although the sufficient indicator "any" is qualifying "moon."

This made this question slightly more confusing.

Thank you for your time and explanation!

Best,

Basia

[KelseyWoods]

Hi Basia,

You are correct that "any" is a sufficient indicator and that it modifies "moon." Since "moon" is the sufficient condition, the necessary condition is "orbits a planet in the solar system." Therefore, for a moon, it is necessary that it orbits a planet in the solar system.

When the explanation says that "every moon necessarily orbits a planet in a solar system," the "necessarily" is modifying "orbits a planet" and indicates that "orbits a planet" is the necessary condition. Which means that "moon" is still the sufficient condition in that statement.

Hope that clears up the confusion!

Best,
Kelsey

[mcdonom4]

Hello!

I was wondering if you could tell me why (B) is correct and (C) is incorrect? After reading the stimulus, I immediately thought that the hole in the argument was that either S4 has only one planet, Alpha, that all the moons orbit, or that there could be other planets in S4, but all the moons orbit only around Alpha. I tried applying conditional reasoning, coming up with:

Moon Orbits a planet in a solar system

But it didn't really clear it up for me. Both (B) and (C) seemed correct, so I just chose one of the two.

[Ricky_Hutchens]

Hi mcdonom4,

I think you've misread the answer. C is correct and B is incorrect. For the conclusion to hold, Alpha must be the only planet in S4. Let's exam B.

If there are 4 moons in S4 and they all orbit the same planet (as B says), then how do we know that planet is Alpha. There might be 100 planets in S4. If all of the moon orbited the same planet, there would only be a 1% chance that that planet is Alpha. So B does not justify the conclusion in the stimulus.

[LustingFor!L]

I diagrammed the following:

P: moon -> orbit some plant in solar system
C: all moons in S4 --> orbit the planet alpha

Can you elaborate more on why B is the incorrect answer. Is alpha an element that we need to link?

[Francis O'Rourke]

Choice (B) does strengthen the conclusion, but it does not justify it. If we assume Choice (B), it may still be the case that every moon orbits a planet Beta in the solar system, in which case we cannot justifiably conclude that all the planets orbit the Planet Alpha.

Planet Alpha is a new element in the conclusion that needs to be linked to justify the conclusion.

[egarcia193]

Hi

I chose answer C but cause I thought it was a little bit better than B but I don't see how B is wrong. If the conclusion is that all moons in s4 all orbit planet Alpha, and every moon in s4 orbits the same planet how does that not prove that all the moons orbit alpha? because if all the moons only orbit one planet and the conclusion tells us that's alpha how does not justify the conclusion? I see how it makes B a better choice as it says what B is kinda driving at but I don't see how B is in itself wrong other than that reason?

[Adam Tyson]

Imagine for a moment, egarcia193, that in solar system S4 there are 9 planets. Those planets are Alpha, Beta, Gamma, Delta, Epsilon, Zeta, Eta, Theta, and Bob. Would knowing that all the moons in S4 orbit the same planet (as each other) prove that they all orbit Alpha? Couldn't they all orbit Bob instead? That's why B only strengthens the conclusion, telling us that all the moons are together around one planet (so there aren't some around Alpha and others around Delta and others around Bob), but doesn't prove the astronaut's conclusion that the one planet they all orbit is Alpha. Because what about Bob?

Remember that we are not going to use the conclusion (they all orbit Alpha) as a premise to support the answer choice here. That's what it looks like you may have done. Instead, take the premises (all moons orbit a planet), add the correct answer (Alpha is the only planet in system S4), and you prove the conclusion (therefore, all the moons in S4 orbit Alpha). Don't use the conclusion to support itself!

I hope that helped. Keep at it!

[egarcia193]

Thanks it made a lot more sense in visualizing everything in the way you described it.