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

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If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

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New post Updated on: 01 Oct 2018, 22:24
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A
B
C
D
E

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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.

Originally posted by kimakim on 07 Sep 2010, 04:32.
Last edited by Bunuel on 01 Oct 2018, 22:24, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

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New post 08 Sep 2010, 08:29
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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. If C, then D. If all of the statements abo  [#permalink]

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New post 07 Sep 2010, 17:56
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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. If C, then D. If all of the statements abo  [#permalink]

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New post 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 statements abo  [#permalink]

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New post 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
Truth Table.jpg [ 59.45 KiB | Viewed 8941 times ]
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Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

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New post 08 Sep 2010, 08:22
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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 statements abo  [#permalink]

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New post 18 Sep 2010, 12:14
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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 statements abo  [#permalink]

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New post 17 Aug 2011, 05:02
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jamifahad 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.


I saw the OA in the mail but C does make sense.

(A) If D, then A
A will definitely result in D doesn't mean someone else can't trigger D. Maybe Z can spawn D. So, we can have D by Z. A is nowhere in the picture.

(B) If not B, then not C.
Same logic as before. C is triggered by B doesn't mean ONLY B can trigger C. GHOST may trigger C. So, we have GHOST and C., and no B. This becomes false.

(C) If not D, then not A.
Definitely true. If we don't see D, it means there CAN't be A. Know this. As soon as A appears, at least B,C,D also appear. Thus, if don't see D, there can't be any A. However, if we see D, there is no guarantee that A is there. CORRECT.

(D) If D, then E.
What is E.

(E)If not A, then not D.
As I said in option "C", D can be spawned by something else. Say GHOST->C->D
Not true.

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

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New post 17 Aug 2011, 06:32
ok here's a simpler way, if you are good with quant inequalities

if A -- > B, if B -- C , If C -- >

which implies if A -- > D

if you negate, then it becomes the opposite ~D -- > ~A which is C
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Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

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New post 17 Aug 2011, 06:47
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viks4gmat wrote:
ok here's a simpler way, if you are good with quant inequalities

if A -- > B, if B -- C , If C -- >

which implies if A -- > D

if you negate, then it becomes the opposite ~D -- > ~A which is C



well i love the Qyant approach: did you mean to say something like:

IF (POSITIVE) A>B>C>D THEN THE IF NOT (NEGATIVE) WILL BE LIKE MULTIPLYING BY -(1) WHICH REVERSES THE INEQUALITY TO IF NOT D>NOT C> NOT B> NOT A
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Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

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New post 17 Aug 2011, 22:20
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dimri10 wrote:
viks4gmat wrote:
ok here's a simpler way, if you are good with quant inequalities

if A -- > B, if B -- C , If C -- >

which implies if A -- > D

if you negate, then it becomes the opposite ~D -- > ~A which is C



well i love the Qyant approach: did you mean to say something like:

IF (POSITIVE) A>B>C>D THEN THE IF NOT (NEGATIVE) WILL BE LIKE MULTIPLYING BY -(1) WHICH REVERSES THE INEQUALITY TO IF NOT D>NOT C> NOT B> NOT A




yup thats pretty much what i intend to say !!!

if A> B> C > D then negating/ NOT-ing the components simply changes the direction of the sign
-A < -B < -C < -D (or -D> -C > -B > -A whichever way you are comfortable reading the equation from )
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Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

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New post 07 Sep 2011, 07:09
good question. i have an even better trick for such questions. i solved the question in 1:17; i could've done that even earlier. here's the trick.

a->b

to find what else can be true, reverse the order of a,b and make them logical negations of themselves.

a->b= b'->a'
"if A, then B" = "if not B, then not A"

e.g. if it is cloudy, it will rain.
if it is not cloudy, then it will not rain (incorrect. we're not sure)
if it is raining, then it is cloudy (incorrect. again may be it also rains when there are no clouds. we don't know)

if it is not raining, then it is not cloudy (bingo! correct ans)
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Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

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New post 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.

The correct answer is C

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

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New post 01 Oct 2018, 18:39
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.
------

Known one.

Why C is right. Because if D did not happen than A did not happen.
Because we know if A were true than D would become true
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Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

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New post 02 Oct 2018, 03:14
Concept of Negation

IF A =B
then Not B=Not A not vice versa
therefore applying the same rule

we can deduce C to be correct answer
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Re: If A, then B. If B, then C. If C, then D. If all of the statements abo &nbs [#permalink] 02 Oct 2018, 03:14
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