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

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If A, then B. If B, then C. If C, then D. If all of the [#permalink] New post 07 Sep 2010, 03:32
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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.
[Reveal] Spoiler: OA
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Re: If A, then B. If B, then C [#permalink] New post 07 Sep 2010, 03:34
IMO B.
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Re: If A, then B. If B, then C [#permalink] New post 07 Sep 2010, 11:44
How this in Critical Reasoning?
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Re: If A, then B. If B, then C [#permalink] New post 07 Sep 2010, 16:56
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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 [#permalink] New post 07 Sep 2010, 21:02
C it is.

Just like what Tej Jay said.
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Re: If A, then B. If B, then C [#permalink] New post 07 Sep 2010, 21:24
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 [#permalink] New post 08 Sep 2010, 01:30
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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
Truth Table.jpg [ 59.45 KiB | Viewed 4565 times ]
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Re: If A, then B. If B, then C [#permalink] New post 08 Sep 2010, 06:50
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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Re: If A, then B. If B, then C [#permalink] New post 08 Sep 2010, 07:22
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 [#permalink] New post 08 Sep 2010, 07:28
Good explanation TehJay. +1 to u!
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Re: If A, then B. If B, then C [#permalink] New post 08 Sep 2010, 07:29
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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?
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Re: If A, then B. If B, then C [#permalink] New post 08 Sep 2010, 08:06
Good one TehJay.
Kudos for you.
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Re: If A, then B. If B, then C [#permalink] New post 08 Sep 2010, 21:35
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 [#permalink] New post 09 Sep 2010, 01:28
kimakim wrote:
The explanation with deserts was really helpful.
Thank you, Kudos for you TehJay!


Glad I could help! :)
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Re: If A, then B. If B, then C [#permalink] New post 13 Sep 2010, 02:20
chose B..But is this critical reasoning?
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Re: If A, then B. If B, then C [#permalink] New post 18 Sep 2010, 11:14
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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] New post 25 Jun 2012, 09:35
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] New post 28 Jun 2012, 03:54
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] New post 09 Oct 2013, 17:32
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