In each of the questions below, some statements are given followed by some conclusions. Assume the statements to be true even if they contradict commonly known facts. Read all the conclusions and decide which logically follow from the statements. **Statements:** $K \geq L M = N Q \geq N R$ II. $Q \leq O$ Which of the conclusions follow?

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In each of the questions below, some statements are given followed by some conclusions. Assume the statements to be true even if they contradict commonly known facts. Read all the conclusions and decide which logically follow from the statements. **Statements:** $K \geq L > M = N < O$; $P > Q \geq N < R$ **Conclusions:** I. $L > R$ II. $Q \leq O$ Which of the conclusions follow?

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**Solution:** 1. From the first statement: $K \geq L > M = N < O$ - This means $K$ is greater than or equal to $L$, which is greater than $M$ and $N$ (equal to each other), and both are less than $O$. 2. From the second statement: $P > Q \geq N < R$ - $P$ is greater than $Q$, which is greater than or equal to $N$, and $N$ is less than $R$. 3. Analyze conclusion I: $L > R$ - From the inequalities, $L > N$ and $N < R$, but no direct comparison between $L$ and $R$ is given. - Since $L > N$ and $N < R$, $L$ could be greater or less than $R$. So, conclusion I does not necessarily follow. 4. Analyze conclusion II: $Q \leq O$ - From the statements, $Q \geq N$ and $N < O$. - But no direct relation between $Q$ and $O$ is established. - $Q$ could be less than, equal to, or greater than $O$. So, conclusion II does not necessarily follow. **Answer:** Neither conclusion I nor conclusion II logically follows from the given statements.

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