Ordered relations: K < L, K > M, M ≥ N, N > O. Which conclusions follow? I) O < M; II) O < K.
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AIf only conclusion I follows
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BIf only conclusion II follows
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CIf both conclusions I and II follow
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DIf neither conclusion I nor II follows
Answer
Correct Answer: If both conclusions I and II follow
Explanation
Introduction / Context:We trace strict and non-strict inequalities through a chain to compare O with M and K.
Given Data / Assumptions:
- K < L, K > M
- M ≥ N
- N > O
Concept / Approach:N > O and M ≥ N together give M > O. Also, K > M and M > O imply K > O.
Step-by-Step Solution: From N > O and M ≥ N ⇒ M > O (I true). From K > M and M > O ⇒ K > O ⇒ O < K (II true).
Verification / Alternative check:Example: O=1, N=2, M=2 (≥N), K=3, L any >K. Both conclusions hold.
Why Other Options Are Wrong:Since both conclusions are forced, “only I/II” or “neither” are incorrect.
Common Pitfalls:Treating ≥ as possible equality with O; transitivity still shows strict greater-than above O.
Final Answer:If both conclusions I and II follow