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A coding sheet gives each relation sign a playing-card suit: '♠' means 'is greater than or equal to', '♣' means 'is greater than', '♥' means 'is equal to', '♦' means 'is less than or equal to', and '✦' means 'is less than'.
Given that 'D ♠ F', 'F ♥ G' and 'G ♠ E' are all true, which conclusion follows?
Conclusions: I. 'D ♣ E'
II. 'D ♥ E'

Competition practiceInequalities
  • AOnly I follows
  • BNeither I nor II follows
  • CEither I or II follows
  • DBoth I and II follow

Step-by-Step Solution

Decoded, the statements are D ≥ F, F = G and G ≥ E, which compose to D ≥ G ≥ E, that is D ≥ E. Every link is non-strict, so nothing stronger is available. Conclusion I decodes to D > E and II to D = E. Neither is forced alone: D = 9, F = G = 3, E = 3 makes I true and II false, while D = F = G = E = 3 makes II true and I false. But D ≥ E means D is above E or equal to it and nothing else, so exactly one of the two must hold — the complementary pair, giving 'either I or II'. 'Only I follows' is the usual error of reading a run of ≥ links as >. 'Both' is impossible since I and II exclude each other.
Answer: C) Either I or II follows

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