Statements: P ≥ R

Question

Statements: P ≥ R < U ≤ M < V ; T ≤ U ; L < M Conclusion I: T < L Conclusion II: V >L

Accepted Answer

Given: $P\ge R< U\le M< V;\; T\le U;\; L< M$. Step-by-step: 1. From $R< U\le M< V$ we have the definite chain $R< U\le M< V$, so in particular $M< V$ and $L< M$ are both true. 2. Conclusion I: $T< L$? We only know $T\le U$ and $L< M$ with $U\le M$. From $T\le U\le M$ and $L< M$ we cannot compare $T$ and $L$ necessarily. Counterexample: let $U=3,\;M=4,\;L=2,\;T=3$. Then $T\le U$ and $L< M$ hold, but $T< L$ is false. Thus $T< L$ does not follow. 3. Conclusion II: $V>L$? Since $L< M$ and $M< V$, by transitivity $L< V$, i.e. $V> L$. This must be true from the given statements. Therefore only Conclusion II follows. FINAL_ANSWER: b

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