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

[mkemp]

Good Afternoon!
This is a general question, and I know it is simple, but I tend to confuse myself with it. When diagramming for questions, do you always automatically take the contrapositive from the statements, or is there a particular keyword for when you know when to do it? For example, here you took the contrapositive of the judges head on one side and the tree on the other, but did not take the contrapositive of the head being on one side and not the other. Thank you for your help!

[Frank Peter]

Hi mkemp,

I would say that developing an instinct for when to diagram the contrapositive comes with experience and exposure to different types of problems on the test. It's certainly good to practice diagramming the contrapositive, but not every problem is going to require taking the contrapositive of a statement in order to get the right answer. I would say that if a stimulus contains multiple conditional statements, there's a higher likelihood that you may need to diagram a contrapositive in order to find the right answer (for example, if the problem is going to entail linking together multiple conditional statements). It's also important to remember to think intuitively about what is being said when you start diagramming conditional reasoning - consider in your own words what is being said. Sometimes taking the contrapositive can aid in that understanding.

[stephalva]

Hi,

I'm having trouble understanding how "None" modifies the necessary condition. Re-reading it, I get it. But I keep making the mistake of modifying the sufficient because it comes right after. How do I avoid this mistake?

[Bob O'Halloran]

Hi Stephalva,
For clarification, are you talking about the 'None' in the stimulus or in the answer choices?

In either case, diagramming may help you avoid the confusion. In this case the word "all" indicates JH as the sufficient condition so

JH---->Tree

and the contrapositive would be

Not Tree-----> Not JH (Answer choice D)

Also take a look at Frank's response above.

Let us know if that helps.
Bob

[cgleeson]

Hi,
I need a clarification, in the stimulus it states "all" the coins with a judge head on 1 side have the tree on the other.
Answer choice D states: "none" with a building have a judge head on the other side. The logical opposite of none is some...the logical opposite of "all" is not all. I realize this is not "Except" question but if it were I would need to employ these logical opposites correct? Thinking like this, when I see all, then a none it causes me concern. Is this something the testmakers will try to employ from time to time? mixing logical opposites?
Thank you in advance

[Robert Carroll]

cgleeson,

"None" is a standard conditional word and something you want to be ready for.

"None of the cards on the board was a diamond"

=

card on the board diamond

So answer choice (D) is saying:

building judge

Contraposing that:

judge building

which is certainly true - according to the stimulus, anything with a judge on one side has a tree, not a building, on the other.

Robert Carroll

[olenka.ballena@macaulay.cuny.edu]

Hi akatormubarez,

The author provides that all of the coins with a judge's head on one side had a tree on the other:

judge's head tree

As you correctly diagrammed, if there is no tree there is no judge's head

tree judge's head

The contrapositive diagram above confirms answer choice D: if there is a building on one side of the coin, that's not a tree, so it would be impossible to find a judge's head on the other side.

Answer choice A is incorrect because an explorer's head on one side of a coin still leaves open the possibility that the other side of the coin will display a tree.

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

~Steve

Hi,

I got this question correct, but I just want to make sure I got it correct for the right reasons. My diagrams and CP's are all correct, but when I'm not sure I used them in the same way you guys have laid out.

I initially kind of somewhat dismissed A because the question stem gave us no information on explore's heads and buildings (nothing specific about buildings, and only that heads cannot be on both sides of the same coin).

I knew from my diagram (JH --> T) that B was a MR, so I eliminated it.

Again, kind of did a preliminary elimination of C because it discussed the explorer's head.

Then for D, I now see that it reflects the contrapositive of JH --> T (NOT t --> NOT JH), but when I picked it, I thought in my mind that D was not possible because any coin with a JH on one side, has to have a tree on the other. So I guess kind of used the original conditional relationship (JH --> T) instead of its CP to choose answer choice D? I could be overthinking this, in which case I apologize! I'm just not sure if I'm explaining this well, but I just wanted to attempt to explain my thought process to ensure I don't get future questions like this wrong.

When I saw E, I again saw it included the explorer's head and dismissed it since we know nothing about that.

Thanks in advance!

[Rachael Wilkenfeld]

Hi olenka,

You have the original statement spot on----Judges head---->tree
The contrapositive would be tree judge's head

Anything that is not a tree would fall into the not tree category---that includes the explorer head and the building. We know none of the coins with either the explorer head or the building have a judge's head on the other side. Those are the only things that must be true, and the only one of those is answer choice (D). I would highly recommend prephrasing using the contrapositive in questions like this so that the correct answer choice jumps out at you a bit more.

Good work!