Direction : In the following questions, the symbols- &, @, % and $ are used…

2021

Direction : In the following questions, the symbols- &, @, % and $ are used with the following meanings as illustrated below.
Study the following information and answer the given questions. In each of the questions given below statements are followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements regarding commonly known facts.
A@B means “All A are B”
A&B means “Only a few A are B”
A$B means “No A is B”
A%B means “Some A is B”

Statement: F%J$G&C@E
I. All C can never be F
II. Some G is not E
III. All F being G is not a possibility
IV. Some J being E is a possibility

  1. A.

    Both III and IV

  2. B.

    Only I

  3. C.

    Both II and III

  4. D.

    Only IV

  5. E.

    Only III

Attempted by 9 students.

Show answer & explanation

Correct answer: A

Concept

In coded syllogism, each symbol fixes one relationship between two sets, and a conclusion is judged in two distinct ways. A definite conclusion ("follows") must hold in EVERY arrangement that the statements allow. A possibility conclusion (the phrasing "is a possibility") needs only ONE valid arrangement in which it can hold. The decoding here is:

  • X@Y = All X are Y

  • X&Y = Only a few X are Y, i.e. Some X are Y and some X are not Y

  • X$Y = No X is Y

  • X%Y = Some X is Y

Application

Decode the chain F%J$G&C@E into separate premises:

  1. F%J : Some F are J.

  2. J$G : No J is G (J and G are completely separate).

  3. G&C : Only a few G are C, so some G are C and some G are not C.

  4. C@E : All C are E.

Now test each conclusion against these premises:

  1. "All C can never be F" claims it is impossible for C to lie inside F. But nothing connects C to F, so an arrangement where every C is also an F can be drawn without breaking any premise. Since that arrangement is allowed, the impossibility claim fails.

  2. "Some G is not E" is a definite claim. The G that are C must be E (since all C are E), but the G that are not C are unconstrained, so an arrangement where every G happens to be E is allowed. Because it need not be true in every arrangement, it is not established.

  3. "All F being G is not a possibility": some F are J, and no J is G, so the F that are J can never be G. At least that part of F stays outside G in every arrangement, making "all F are G" genuinely impossible. The impossibility is established, so this holds.

  4. "Some J being E is a possibility": no premise blocks J from overlapping E, so an arrangement in which some J are E can be drawn. The possibility is established, so this holds.

Cross-check

Conclusion (i) is rejected because the opposite arrangement is allowed; conclusion (ii) is rejected because it is not forced in every case. Conclusion (iii) is a forced impossibility and conclusion (iv) is a valid possibility, so exactly the third and fourth conclusions are the ones that hold.

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