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

Nikki Siclunov
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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 :arrow: 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!
Nikki Siclunov
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Blueballoon5%
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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
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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
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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
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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 :arrow: certain

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

~Steve
Steve Stein
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kim4956
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Continuing the discussion, what's the difference btwn answer choices (c) and (d)?

Thanks!
Kim
Nikki Siclunov
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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 :dblline: EH
JH :dblline: JH
EH :dblline: EH
JH :arrow: T

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

T :dblline: 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 :dblline: 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!
Nikki Siclunov
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Blueballoon5%
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Lucas Moreau wrote: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!