Discussion
Statement: P ≤ Q, Q > R, T ≥ U, S > R, T = S
Conclusions:
I. R ≥ U
II. P ≤ U
Answer: D
Correct answer: Neither conclusion a nor b follows
The statements are \( P \le Q \), \( Q > R \), \( T \ge U \), \( S > R \) and \( T = S \). Merging T with S, the picture is R sitting below both Q and S, with P at or below Q and U at or below S: \[ P \le Q > R < S = T \ge U. \] There are two reversals here, at Q and at R.
I. \( R \ge U \): R sits below S and U sits at or below S, so both hang beneath the same element from the same side. With \( S = 10 \), \( R = 9, U = 1 \) and \( R = 1, U = 9 \) both satisfy the statements. Not determined.
II. \( P \le U \): P is capped by Q, U is capped by S, and the two caps are joined only through R, which is below both. Nothing carries across. Not determined.
Neither conclusion follows. Every element here is bounded from above and nothing is bounded from below, which is exactly the arrangement in which almost no comparison can be made.
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