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# If A, then B. If B, then C. If C, then D. If all of the

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Intern
Joined: 24 Jun 2010
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If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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07 Sep 2010, 04:32
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48% (00:39) correct 52% (00:49) wrong based on 320 sessions

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If A, then B.
If B, then C.
If C, then D.
If all of the statements above are true, which of the following must also be true?

(A) If D, then A.
(B) If not B, then not C.
(C) If not D, then not A.
(D) If D, then E.
(E) If not A, then not D.

Why is the official answer C ?

For example, choice B could be correct too. If not B then not C.
Manager
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Posts: 190
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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08 Sep 2010, 08:29
7
1
utin wrote:
TehJay wrote:
kimakim wrote:
If A, then B.
If B, then C.
If C, then D.
If all of the statements above are true, which of the following must also be true?

(A) If D, then A.
(B) If not B, then not C.
(C) If not D, then not A.
(D) If D, then E.
(E) If not A, then not D.

Why is the official answer C ?

For example, choice B could be correct too. If not B then not C.

We're given A -> B, B -> C, and C -> D, and told they're all true. Since they're all true, you can say A -> D. Then by the law of contrapositive, ~D -> ~A. The answer is (C).

(B) isn't correct - this is the inverse of B -> C and does not have the same truth table.

CAN'T UNDERSTAND STILL!!!

Ok, consider a simple example:

If I eat dinner now, I will eat dessert later. (A -> B)

You're told this is a TRUE statement - in other words, eating dinner absolutely, positively, no question about it, 100% results in eating dessert after. There's no possible situation that can exist where I will eat dinner now and then NOT eat dessert later.

Now consider the below statements:

If don't eat dessert later, I didn't eat dinner now. (contrapositive: ~B -> ~A)

Since we KNOW FOR A FACT that eating dinner now results in eating dessert later, we can conclude without a doubt that if I don't eat dessert, I most definitely did not eat dinner (because if I had eaten dinner, I would have eaten dessert). This is called the contrapositive and is logically equivalent to the original statement. (This is answer C)

If I don't eat dinner now, I won't eat dessert later. (inverse: ~A -> ~B)

We know for a fact that eating dinner will lead to eating dessert. However, we know absolutely nothing about the result of NOT eating dinner. I didn't say to you that I would ONLY eat dessert if I eat dinner first - only that I would definitely eat it after eating dinner. This statement is not logically equivalent to the original. This is called the inverse, and is answer B.

Does this help?
##### General Discussion
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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07 Sep 2010, 12:44
How this in Critical Reasoning?
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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07 Sep 2010, 17:56
5
2
kimakim wrote:
If A, then B.
If B, then C.
If C, then D.
If all of the statements above are true, which of the following must also be true?

(A) If D, then A.
(B) If not B, then not C.
(C) If not D, then not A.
(D) If D, then E.
(E) If not A, then not D.

Why is the official answer C ?

For example, choice B could be correct too. If not B then not C.

We're given A -> B, B -> C, and C -> D, and told they're all true. Since they're all true, you can say A -> D. Then by the law of contrapositive, ~D -> ~A. The answer is (C).

(B) isn't correct - this is the inverse of B -> C and does not have the same truth table.
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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07 Sep 2010, 22:02
C it is.

Just like what Tej Jay said.
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Joined: 24 Jun 2010
Posts: 8
Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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07 Sep 2010, 22:24
TehJay wrote:
kimakim wrote:

We're given A -> B, B -> C, and C -> D, and told they're all true. Since they're all true, you can say A -> D. Then by the law of contrapositive, ~D -> ~A. The answer is (C).

(B) isn't correct - this is the inverse of B -> C and does not have the same truth table.

Yes, the logic is right, if we assume that ALL of the statement should be exist at the same time.
But consider if there is only C. Then C->D, and we don;t need A or B to come up with D. Hence if "not D" doesn't imply "not A".

On the other hand answer B "If not B then not C" is right, when we assume that all statements can exist independently of each other.

So, I am still confused
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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08 Sep 2010, 02:30
2
kimakim wrote:
TehJay wrote:
kimakim wrote:

We're given A -> B, B -> C, and C -> D, and told they're all true. Since they're all true, you can say A -> D. Then by the law of contrapositive, ~D -> ~A. The answer is (C).

(B) isn't correct - this is the inverse of B -> C and does not have the same truth table.

Yes, the logic is right, if we assume that ALL of the statement should be exist at the same time.
But consider if there is only C. Then C->D, and we don;t need A or B to come up with D. Hence if "not D" doesn't imply "not A".

On the other hand answer B "If not B then not C" is right, when we assume that all statements can exist independently of each other.

So, I am still confused

You're told that all of them are true, so you can't just take them independently and pretend that A doesn't exist. Also, irregardless of whether you're looking at A or not, (B) cannot be correct. This is the logical inverse, which is a fallacy. In logic, when dealing with implications, p -> q is equivalent to ~q -> ~p, but not equivalent to ~p -> ~q (inverse) or q -> p (converse). To see this, you can draw up the truth tables:

Attachment:

Truth Table.jpg [ 59.45 KiB | Viewed 8360 times ]
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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08 Sep 2010, 07:50
TehJay wrote:
kimakim wrote:
If A, then B.
If B, then C.
If C, then D.
If all of the statements above are true, which of the following must also be true?

(A) If D, then A.
(B) If not B, then not C.
(C) If not D, then not A.
(D) If D, then E.
(E) If not A, then not D.

Why is the official answer C ?

For example, choice B could be correct too. If not B then not C.

We're given A -> B, B -> C, and C -> D, and told they're all true. Since they're all true, you can say A -> D. Then by the law of contrapositive, ~D -> ~A. The answer is (C).

(B) isn't correct - this is the inverse of B -> C and does not have the same truth table.

CAN'T UNDERSTAND STILL!!!
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Posts: 774
Location: London
Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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08 Sep 2010, 08:22
1
the statement "if A then B" is exactly the mathematical equation (A or not(B))

the three statements together, are three simultaneous equations which solve to give (A or (not(D)) [which logical deduction can tell you]

and finally :

(A or Not(D)) = (not(not(A)) or not(D)) = (not(D) or not(not(A))) = "if not D then not A"
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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08 Sep 2010, 08:28
Good explanation TehJay. +1 to u!
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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08 Sep 2010, 09:06
Good one TehJay.
Kudos for you.
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Joined: 24 Jun 2010
Posts: 8
Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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08 Sep 2010, 22:35
The explanation with deserts was really helpful.
Thank you, Kudos for you TehJay!
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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09 Sep 2010, 02:28
kimakim wrote:
The explanation with deserts was really helpful.
Thank you, Kudos for you TehJay!

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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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13 Sep 2010, 03:20
chose B..But is this critical reasoning?
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Class of 2012
Great Lakes Institute of Management
http://greatlakes.edu.in

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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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18 Sep 2010, 12:14
1
I learned this today (forgot the original poster but kudos to him). His/her quote went as
If A then B , could be rephrased as if Not B then Not A and if B then may be A.

Take the example of: If I am in France, I am in Europe

If I am not in Europe, I am not in France. ( Not B then Not A)

If I am in Europe, I may be in France ( B then may be A).

All other violate this logical rule or add extra information.

So in the given example by reversing all the signs we get....
~D => ~C
~C => ~B
~B => ~A
Thus simply substituting....
~D => ~A
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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25 Jun 2012, 10:35
Take A, B, C & D as people.
1. A --> B: If Alice comes then Bella will come.
2. B --> C: If Bella comes then Charlie will come.
3. C --> D: If Charlie comes then Dan will come.

Now, per OA, if Dan doesn't come, what impact does it have on Alice?
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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28 Jun 2012, 04:54
a->b->c->d
so, a->d
contrapositive: not d -> not a
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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10 Aug 2015, 16:23
Request you not to write your queries/answers/opinions in question window. It prevents ppl from analysing the question. The whole purpose of GMAT Club forum goes wasted by doing so.
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Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

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03 Aug 2018, 18:21
kimakim wrote:
If A, then B.
If B, then C.
If C, then D.
If all of the statements above are true, which of the following must also be true?

(A) If D, then A.
(B) If not B, then not C.
(C) If not D, then not A.
(D) If D, then E.
(E) If not A, then not D.

Why is the official answer C ?

For example, choice B could be correct too. If not B then not C.

This question requires a good calculation in the background. One thing to remember is "if A then B does not imply the presence of B is only by A". It only implies that "if A is present, then B must be present".

Option A is incorrect because D might not necessarily imply that C is present and so B and A.
Option B is incorrect as if not B , there are chances of C to be present. Not necessarily true.
Option C is correct as if not D then no C.There is no B without C. There is no A without B.
Option D is irrelevant
Option E is also incorrect as if not A, there can be B. So with C and D.

Thanks,
Uma
Re: If A, then B. If B, then C. If C, then D. If all of the &nbs [#permalink] 03 Aug 2018, 18:21
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