In the questions given below, certain symbols are used with different…

2025

In the questions given below, certain symbols are used with different meanings, as indicated below. Assuming the given statements to be true, decide which of the two given conclusions, I and II, is/are definitely true, even if they seem to differ from commonly known facts.

  • A + B means A is greater than B.

  • A - B means A is equal to B.

  • A = B means A is not equal to B.

  • A * B means A is greater than or equal to B.

  • A / B means A is not less than or equal to B (that is, A is greater than B).

Statements: Q + P, S / Q, R = S

  1. Conclusion I: S + P

  2. Conclusion II: R = P

  1. A.

    Only conclusion-1 is true

  2. B.

    Only conclusion-2 is true

  3. C.

    Neither conclusion-1 nor 2 is true

  4. D.

    Both conclusion-1 and 2 are true

Show answer & explanation

Correct answer: A

Concept: In coded statement-and-conclusion reasoning, each symbol stands for a relational operator (>, <, =, ≠, ≥, ≤). Decode every statement into its true relation, chain the relations using transitivity (if A > B and B > C, then A > C), and only accept a conclusion as "definitely true" if it holds in every arrangement of values consistent with the statements — not merely in one possible case.

Application: Decode the statements using the given definitions.

  1. Q + P means Q is greater than P, so Q > P.

  2. S / Q means S is greater than Q, so S > Q.

  3. R = S means R is not equal to S, so R ≠ S.

  4. Chaining Q > P with S > Q by transitivity: S > Q > P, which gives S > P directly.

  5. Conclusion I (S + P, i.e., S > P) follows directly from this chain, so it is definitely true.

  6. Conclusion II (R = P, i.e., R ≠ P) relies only on R ≠ S, which places no constraint on R relative to P — R could still equal P without contradicting any statement, so conclusion II is not guaranteed.

Cross-check: Take P = 1, Q = 2, S = 3 (satisfies Q > P and S > Q) and R = 1 (satisfies R ≠ S, since 1 ≠ 3). Here S > P (3 > 1) holds as expected, but R = P (1 = 1), so R ≠ P fails in this valid arrangement — confirming conclusion II is not universally guaranteed while conclusion I always is.

Result: Only conclusion I is definitely true.

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