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In one section of a paper the relation signs are swapped for marks: '§' means 'is greater than or equal to', '¶' means 'is less than or equal to', '¤' means 'is equal to', '†' means 'is greater than', and '‡' means 'is less than'.
Given that 'V † W', 'W ¤ X' and 'X § Y' are all true, which of the following does NOT follow?

Competition practiceInequalities
  • AV † Y
  • BV † X
  • CW § Y
  • DY ¤ X

Step-by-Step Solution

Decoded, the statements are V > W, W = X and X ≥ Y, so the chain is V > W = X ≥ Y. 'V † X' (V > X) follows, since W = X turns V > W into V > X. 'V † Y' (V > Y) follows, since V > X and X ≥ Y compose to a strict result. 'W § Y' (W ≥ Y) follows, because W = X and X ≥ Y give W ≥ Y. But 'Y ¤ X' claims Y = X, and all that is given is X ≥ Y, which also allows X strictly above Y — X = 9, Y = 2 satisfies every statement while Y = X fails. So that is the one conclusion the chain does not support: it would require the non-strict link X ≥ Y to be an equality, which is only one of its two possibilities.
Answer: D) Y ¤ X

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