#14 - Among a sample of diverse coins from an unfamiliar

[Nikki Siclunov]

Hi rameday,

Let's think about what this statement means in conditional terms:

None of them have heads on both sides

So, if a coin has a head on one side, it does not have a head on the other side:

Head on one side NO Head on the other side

When combined with the other conditional statement in the stimulus, we can prove that answer choice (D) states a contrapositive claim.

Just a reminder: this question - as well as every other question from your Homework - is explained on the Online Student Center.

Thanks!

[Blueballoon5%]

How do I translate answer C into a conditional statement: "None of those with a tree on one side have an explorer's head on the other." What does the "none" modify in this sentence?

[Lucas Moreau]

Hello, Blueballoon,

C could become a conditional statement like "If a coin has a tree on one side, it does not have an explorer's head on the other." That is the same as saying that no coins with a tree on one side have an explorer's head on the other. The "none" means "no coins that have a tree on one side".

Hope that helps,
Lucas Moreau

[skiiam]

Could you explain why "none" modifies the necessary, as in (C) and (E) rather than the sufficient in this case (even though it looks like none is modifying the sufficient)?

I continue to make this mistake and no sure what I'm doing wrong. I understand order of conditions does not matter. But I still don't understand why none/no modifies the necessary condition.

Another similar problem: "But no expert is certain of being able to solve someone else's problem"
The answer is: E -> ~SSEP.
But I wrote ~E -> SSEP.

How do I avoid this mistake?

[Steve Stein]

Hey skiiam,

Thanks for your response--that's a great question, the mistake you mentioned is a very common one. For the example you brought up, try changing the sentence to an "if...then" statement; it may quickly become much more clear:

No expert can be certain.

What are they really saying? if you're an expert, you can't be certain!

Expert certain

I hope that's helpful! Please let me know whether this is clear--thanks!

~Steve

[kim4956]

Continuing the discussion, what's the difference btwn answer choices (c) and (d)?

Thanks!
Kim

[Nikki Siclunov]

Hi Kim,

From the stimulus, we know the following: each face of any coin has one of the following: JH, EH, B, T. According to the last sentence, the following conditional relationships can be established:

JH EH
JH JH
EH EH
JH T

Answer choice (C) states that no coin with a T on one side has EH on the other:

T EH

We cannot prove that to be true. Note that having a T on one side does not mean that you need to have JH on the other (that would be a Mistaken Reversal of the last rule). So, it's entirely possible that some coins with a T on one side have EH on the other.

Answer choice (D) states that none of those with a B on one side have a JH on the other:

B JH

This is provably true. From the last rule, we know that any coin with a JH on one side must have a T on the other, not B. Therefore, answer choice (D) must be true and is therefore correct.

Let me know if this answers you question.

Thanks!

[Blueballoon5%]

Hello, Blueballoon,

C could become a conditional statement like "If a coin has a tree on one side, it does not have an explorer's head on the other." That is the same as saying that no coins with a tree on one side have an explorer's head on the other. The "none" means "no coins that have a tree on one side".

Hope that helps,
Lucas Moreau

Thanks Lucas!

[lilglowx]

I'm not sure if I'm grasping the concept/logic

JH <--I--> EH (no heads on both sides of coin)
JH --> Tree (if judgehead, then tree)

Contrapositive?: NOT tree ---> NOT JH
and NOT tree automatically signifies Building because it CANNOT be EH (explorer's head) on the other side?
So this matches answer D "None of those with a building on one side have a judge’s head on the other".



Is answer A "All those with an explorer’s head on one side have a building on the other" wrong because the stimulus provides no support whatsoever , and is a false assumption?

[Jeremy Press]

Hi lilglowx,

You're on the right track for sure!

I want to correct one thing in your post. In the contrapositive of the JH Tree conditional, "Not Tree" could be anything that is not a tree: a building, an explorer's head, even a judge's head. In other words, if there's a building on one side, a judge's head can't be on the other side (that validates answer choice D, as you stated). But also, if there's an explorer's head or a judge's head on one side, there can't be a judge's head on the other side. Does that make sense?

The reason answer choice A is not correct is that all we know from the stimulus is that, if an explorer's head is on one side, there cannot be another explorer's head or a judge's head (no heads at all) on the other side. But there still could be either a tree or a building on the other side.

I hope this helps!

Jeremy