G is shorter than FStudy the following information carefully and answer the following question., B, C, D, E, F, G, and H are eight students, each having a different height.
(i) D is shorter than A but taller than G.
(ii) E is taller than H but shorter than C.
(iii) B is shorter than D but taller than F
(iv) C is shorter than G.
(v) G is not as tall as F.
Which of the following statements is definitely INCORRECT?

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  1. G is shorter than F
  2. C is shorter than F.
  3. F is taller than C
  4. None of the given options

Answer (Detailed Solution Below)

Option 4 : None of the given options
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Let's analyze the given statements to determine the relative heights of the eight students: A, B, C, D, E, F, G, H.

(i) D is shorter than A but taller than G.

This can be written as: A > D > G

(ii) E is taller than H but shorter than C.

This can be written as: C > E > H

(iii) B is shorter than D but taller than F.

This can be written as: D > B > F

(iv) C is shorter than G.

This can be written as: G > C

(v) G is not as tall as F.

This means G is shorter than F: F > G

Now, let's combine these inequalities to establish the overall height order:

From (iv) and (ii):
G > C > E > H

From (v) and the above:
F > G > C > E > H

From (i):
A > D > G
Combining this with F > G, we know G is shorter than D and F. Now we need to place D relative to F.

From (iii):
D > B > F
This definitively places D as taller than F.

So, the complete combined order is:

A > D > B > F > G > C > E > H

Now, let's evaluate each of the given options based on this established order:

  1. G is shorter than F.
    From our order (F > G), this statement is TRUE.
  2. C is shorter than F.
    From our order (F > G > C), this statement is TRUE.
  3. F is taller than C.
    From our order (F > G > C), this statement is TRUE

Since all the statements (1, 2, and 3) are true based on the provided information.

Hence, the correct answer is "Option 4".

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