In the question symbols $, #, % are used for different meaning as follows. $…

2024

In the question symbols $, #, % are used for different meaning as follows.

$ means ‘neither greater nor equal to’.

# means ‘neither greater nor smaller than’.

% means ‘neither smaller nor equal to’.

In the following question assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true.

Statements: T % I, I # L, L % U

Conclusions:

T $ L

U $ T

  1. A.

    Only I is true

  2. B.

    Only II is true

  3. C.

    Either I or II is true

  4. D.

    Both I and II are true

Attempted by 1 students.

Show answer & explanation

Correct answer: B

Concept:

In coded-inequality problems, each symbol stands for a standard relational operator. Once every statement is rewritten with real operators, the statements can usually be chained (transitively, through any shared term) into one combined ordering. Each conclusion is then checked against that single ordering: it is definitely true only if it is a direct consequence of the chain, and definitely false if it states the opposite relation. The 'Either/Or' verdict applies only when two conclusions form a complementary pair about the same two terms (together they cover every possible relation between those terms, e.g. '>' and '≤'), with neither following individually — not whenever two conclusions merely exist.

Application:

  1. Substitute the coded symbols with their real meanings: $ = less than (<), # = equal to (=), % = greater than (>).

  2. Rewrite the three statements: T % I → T > I; I # L → I = L; L % U → L > U.

  3. Chain them through the shared terms: since I = L, the first statement T > I becomes T > L; combined with L > U, the full ordering is T > L > U (with I = L throughout).

  4. Check Conclusion I (T $ L, i.e. T < L) against this ordering: the chain gives the opposite relation between T and L, so Conclusion I does not follow.

  5. Check Conclusion II (U $ T, i.e. U < T) against this ordering: the chain T > L > U directly gives T > U, i.e. U < T, so Conclusion II follows.

  6. Since exactly one conclusion follows the chain and the two conclusions are not a complementary either/or pair (they compare different term-pairs), only Conclusion II is definitely true.

Cross-check:

Assign sample values consistent with the derived ordering: let I = L = 5, T = 6, U = 4. Verify each statement: T > I (6 > 5) ✓, I = L (5 = 5) ✓, L > U (5 > 4) ✓. Now test the conclusions: Conclusion I says T < L, i.e. 6 < 5 — false. Conclusion II says U < T, i.e. 4 < 6 — true. This numeric check confirms only Conclusion II holds.

Only Conclusion II is true — matching the option “Only II is true”.

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