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

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:

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"

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 )

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)

The chain of logical statements can be represented as follows:
A → B → C → D
We can use the transitive property of implication to combine the statements into a single implication:
A → D
Therefore, if A is true, then D must also be true.

(A) If D, then A.
This statement cannot be concluded from the given information. We know that A implies D, but we cannot infer that D implies A.

(B) If not B, then not C.
This statement is true by contrapositive. If C is true, then B must be true, and if B is not true, then C cannot be true.

(C) If not D, then not A.
This statement is false. The contrapositive of A → D is ¬D → ¬A. Therefore, if D is not true, we cannot conclude anything about whether A is true or not.

(D) If D, then E.
This statement cannot be concluded from the given information. There is no logical connection between D and E in the statements given.

(E) If not A, then not D.
This statement is false. The contrapositive of A → D is ¬D → ¬A. Therefore, if A is not true, we cannot conclude anything about whether D is true or not.

'


In case of answer choice C, Would it be correct to say " event C has occurred, which doesn't necessarily mean event B has also occurred". As event B is leading to event C but not vice-versa?

In simple words it is the application of law of contra-positive.Consider an example: If it is raining then there is cloud and its contra-positive is If there is no cloud then there is no raining. Same logic gives you C. If no D then no A

Still confused!

With the very same logic, option B and E also seem to be correct! Why only C?

While figuring out the answer, I had four things before me- a cup, a spoon, a plate, and a bottle of water. I assumed the cup is A, spoon is B, plate is C and bottle is D. As per the conditions, these are what I concluded.
1. If you want the cup, you must have the spoon. If you want spoon, you must have the plate. If you need plate, you must have bottle. Therefore, someone who just wants the cup will have spoon, plate and bottle.
2. Now, ignore the cup. Say, you need the spoon. So you must have the plate, and to have the plate, you must own the bottle. So a spoon owner will have plate and bottle too.
3. Same logic when applied if I need the plate only, I must own the bottle too.
4. Now, what if I need the bottle alone? In this case, there is no prerequisite.
As per (B), if you don't have spoon, you won't have plate. I can have the plate and bottle just, why does spoon become important here? (conclusion 3)
In (E), if not cup, then not bottle. Why not? I want the bottle alone and as discussed previously, I can own bottle without prerequisites. (conclusion 4)
But in (C), if not bottle, then no cup. Yes. To own a cup, you must have not just the bottle, but every other stuffs too. Therefore, (C) is right. (conclusion 1)

I hope this helps.

­Rewriting Question stem as if loop
if(A)
----if(B)
--------if(C)
------------D
--------else
------------May be not C, May be E or F(so when it's if not C, then it may not be not D)
----else
--------May be not B, May be F or G (so when it's if not B, then it may not be not C)
else
----May be not A, May be G or H (so when it's if not A, then it may not be not B)

But when your output is not D
if (C) returns --> not C or E or F
if (B) returns --> not B or F or G
if (A) returns --> not A or G or H

I didn't get it. Why not A? if not A then Not D. Doesn't it clearly say A>B>C>D?

The converse of "If A, then D", which is "If D, then A", does not have to be true. For example, "If x = 2, then x is prime", however saying if x is prime it is 2 would not be correct.

Assume, A, B, C, D in concentric circles, with D being the largest and A the smallest. (D > C > B > A)
A) If it is in Circle D then it may not be in Circle A. (Option is Out)
B) If it is not in Circle B then it may still be in Circle C. (Option is Out)
C) If it is not in Circle D then it cannot be in Circle A. (This is the answer)
D) Nothing about E is mentioned in the question stem. (Option is Out)
E) If not in Circle A then there is still a possibility of it being in Circle D. (Option is Out)