Grouping Setup Practice Drill #2

[sgowani]

I am having trouble in reaching an answer to the following question:

Grouping Setup Practice Drill Answer Key, Item #2 in Chapter 5, page 274

I know how to diagram the laws:

A------> F and E (cross)
L------> E and M (cross)
O or S ------> A

I understand that why A and L cannot be offered together.
I was able to eliminate the answer choices e) and a) by myself, but I don't understand the explanation given in the book for the elimination of the other answers.
Can you please help me with this?

Thanks a lot

[Dave Killoran]

Hi S,

The correct answer to this question will be something that Could Be True. The incorrect answers will then be things that Cannot Be True.

We know from the question stem that L is offered, and that impacts answer choices (C) and (D), which are both incorrect:

Answer choice (C): The second rule states that, "If law is offered, then economics is also offered but marketing is not." So, in this question, since L is offered, we know that M is not. This answer choice contradicts that statement by saying M is offered, which Cannot Be True and is therefore incorrect.

Answer choice (D): From our inferences, when L is offered, A is not offered. That information can be linked with the third rule, which states, "If operations or sales is offered, then accounting is also offered." Since A is not offered in this question, via the contrapositive we can determine that O and S are not offered. This answer choice states that O is offered, which cannot occur and thus this answer is incorrect.

Answer choice (B) can occur, and is thus correct.

Please let me know if that helps. Thanks!

[sgowani]

Great!
Thanks

[lguenst]

Hello,
I do not understand how the answer to this question is B? Can you please show me a diagram or explanation to how this "could be true".
Thank you,
Lisa

[Nikki Siclunov]

Hi Lisa,

Thanks for your question. If L is offered, the following chain can be created using the contrapositives in the main diagram:

L E NOT A NOT O and NOT S

also:

L NOT M (according to the second rule)

As Dave explained in an earlier post, this eliminates answer choices (A), (C), (D) and (E). Regarding answer choice (B), your question is why (B) could be true. Well, F could be offered: there is no reason why it can't be. The chain we just made does not specify anything that must be true about F. Indeed, all we know about F is that if A is offered, F must be offered as well:

A F

If L is offered, we know for sure that A is not (L E NOT A). That does not mean that F cannot be offered: to infer so would be to make a Mistaken Negation! F can be offered even if A is not offered.

Check out the following analogy:

To go to law school, you must take the LSAT (LS LSAT). But, if I told you that I am not in law school, you cannot logically conclude that I didn't take the LSAT (that would be a Mistaken Negation).

Does that clear things up?

Thanks!

[Echx73]

Qustion:

Is there a contrapositive to the following statements?

(Found on Page 274 LGB)
"If accounting is offered, then fiannce is also offered but economics is not"

"If law is offered, then economics is also offered but marketing is not'

Thank you for your help.

[Ladan Soleimani]

Hey Echx73

Every conditional statement will have a contrapositive. You may not need to write out the contrapositive to answer the question or do the game, but there will always be one and you always find it the same way. Flip the statement and negate both side. Also, with statements with multiple terms any 'ands' become 'ors' and vice versa.

So for your statements:

"If accounting is offered, then finance is also offered but economics is not"

A F + E Contrapositive: F or E A

"If law is offered, then economics is also offered but marketing is not'

L E + M Contrapositive: E or M L

I hope this helps!
Ladan

[MBG13]

The answer and explanation confuses me.

The book explains that the rule set up is as follows which I can follow:

O F
or ----> A ----> and
S E

And

E
L -----> and
M

If you do the contrapositive of the second rule it is represented as:

E
or ------> L
M

I'm presuming that you can link this contrapositve with the first one which look like this:

O F
or ----> A ----> and
S -E
or ------> -L
M

So my question is how is "finance is offered" the correct answer if when you do the contrapositive of above is if L, then not F

What am I doing wrong. (Sorry for the long winded post)

[Dave Killoran]

Hi MBG,

I made a few formatting changes to your post, to help readability. I hope that's ok!

Let me start by mentioning something in your final diagram that is interesting beyond this drill. Note that your second to last necessary condition links one condition (F and E) with a second condition (E or M) through the common variable E. That's totally acceptable, and a good eye on your part to see the linkage. But, the occurrence of A triggers both F and E. The occurrence of E then meets the condition of "E or M", which means that at that point, L would be known to occur. Basically, because E L, once you have E then you can just add the arrow to L, and you don't have to worry about the M portion in that particular diagram.

Ok, that aside, let's look at the question attached to this drill. The first thing is, what are we being asked? "Must Be False EXCEPT" is identical to "Cannot Be True EXCEPT," which means that the 4 incorrect answer are Cannot Be True, and the 1 correct answer is Could Be True. This means that in this question, Finance being offered could be true, not that it has to be true. I'm thinking that might actually resolve your question. Am I correct? If not, let me know and we'll walk through the rest of the problem.

Thanks!

[Echx73]

Hi Dave,

I am just went back over this question and wanted to solidify something. If we were asked, "If E is offered, what must be true. The only thing we can infer is E is offered and A, O and S are not offered. (I know this is simple, but just wanted to confirm.)

Eric