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The substitutions below are in force for this question only: '⊕' means 'is greater than', '⊖' means 'is less than', '⊙' means 'is equal to', '⊞' means 'is greater than or equal to', and '⊟' means 'is less than or equal to'.
Given that 'S ⊖ T', 'T ⊞ U' and 'U ⊖ V' are all true, which conclusion follows?
Conclusions: I. 'S ⊖ U'
II. 'T ⊕ V'

Competition practiceInequalities
  • AOnly I follows
  • BOnly II follows
  • CNeither I nor II follows
  • DBoth I and II follow

Step-by-Step Solution

Decoded, the statements are S < T, T ≥ U and U < V. Conclusion I claims S < U, but S < T and T ≥ U both point up towards T and never compare S with U: S = 1, T = 9, U = 4 makes I true while S = 6, T = 9, U = 4 makes it false. Conclusion II claims T > V, but T ≥ U and U < V leave V free above or below T: T = 9, U = 4, V = 5 makes II true while T = 9, U = 4, V = 40 makes it false. Neither follows. 'Only I follows' is what a solver gets by misreading 'T ⊞ U' as T ≤ U, since S < T ≤ U would genuinely give S < U. 'Both' comes from reading the three statements as a single run in one sense.
Answer: C) Neither I nor II follows

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