Discussion
Statement: A ≥ B, C = D, E > F, E ≥ D, B > C
Conclusions:
I. D > F
II. C ≥ F
Answer: D
Correct answer: Neither conclusion a nor b follows
The statements are \( A \ge B \), \( C = D \), \( E > F \), \( E \ge D \) and \( B > C \). Assembling them gives \( A \ge B > C = D \), with E standing at or above D and F below E: \[ E \ge D = C, \qquad E > F. \]
Both conclusions compare something in the C–D pair with F, and both fail for the same reason: D and F are attached to E from the same side, D at or below it and F strictly below it, which fixes no order between them.
I. \( D > F \): with \( E = 10 \), take \( D = 9, F = 1 \) and the conclusion holds; take \( D = 1, F = 9 \) and it fails. Both satisfy every statement. Not determined.
II. \( C \ge F \): C equals D, so this is the same comparison in weak form, and the same two cases defeat it. Not determined.
Neither conclusion follows.
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