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Triangles and a circle stand in for the five relation signs: '△' means 'is greater than', '▽' means 'is less than', '▷' means 'is greater than or equal to', '◁' means 'is less than or equal to', and '○' means 'is equal to'.
Given that 'A △ B', 'B ▷ C' and 'C ○ D' are all true, which conclusion follows?
Conclusions: I. 'A △ D'
II. 'B ▷ D'

Competition practiceInequalities
  • AOnly I follows
  • BOnly II follows
  • CBoth I and II follow
  • DNeither I nor II follows

Step-by-Step Solution

Decoded, the statements are A > B, B ≥ C and C = D, so the chain is A > B ≥ C = D. Conclusion II decodes to B ≥ D: B ≥ C and C = D give B ≥ D, so II follows. Conclusion I decodes to A > D: A > B and B ≥ D compose to a strict result because the run contains the strict link A > B, so I follows. Both hold. 'Only II follows' is the trap for a solver who thinks the non-strict link B ≥ C strips the strictness out of A > B — it does not, since one strict link anywhere in a same-sense run is enough. 'Only I follows' comes from reading '▷' as strictly greater and then judging B ≥ D too weak to state. 'Neither' comes from treating C = D as a break.
Answer: C) Both I and II follow

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