Direction : Read the given information carefully and answer the questions…

Concept

In coded-inequality reasoning, each symbol is first converted into a plain mathematical relation (>, <, =, ≥, ≤). A conclusion is true only when the statements force it through a single unbroken chain; any gap left by the symbols leaves the conclusion not definite. Two combining rules apply: a chain stays strict (>) if at least one link is strict, and a greater-or-equal link can never overturn a strict greater-than already established.

Decode the symbols

• A%B: B is neither smaller nor greater than A, so A = B.

• A&B: B is neither greater nor equal to A, so B < A (A > B).

• A*B: B is neither smaller nor equal to A, so B > A (A < B).

• A$B: B is not greater than A, so B ≤ A (A ≥ B).

• AαB: B is not smaller than A, so B ≥ A (A ≤ B).

Decode the statements

• P*D$C%B$A → P < D, D ≥ C, C = B, B ≥ A.

• H$T&Y%D → H ≥ T, T > Y, Y = D.

• K*UαW%P → K < U, U ≤ W, W = P.

Application — test each conclusion

1. Conclusion I (D&U means D > U): W = P and P < D give D > W. Since U ≤ W, it follows U ≤ W < D, so D > U. Definite → I is true.

2. Conclusion II (B*T means B < T): T > Y and Y = D give T > D. D ≥ C and C = B give D ≥ B. Combining, T > D ≥ B, so T > B, i.e. B < T. Definite → II is true.

3. Conclusion III (H&K means H > K): chain H ≥ T > Y = D > P = W ≥ U > K. At least one strict link (T > Y, D > P, U > K) makes the whole chain strict, so H > K. Definite → III is true.

Result

All three conclusions are definitely true, so the answer is “All are true”.