Given the statements: - $I \geq J = K M \geq N$ - $I L$ II. $N L$ III. $I M$ IV. $J

Question

Given the statements: - $I \geq J = K < L$ - $L > M \geq N$ - $I < O$ Evaluate the following conclusions: I. $O > L$ II. $N > L$ III. $I > M$ IV. $J < N$ Which of the conclusions follow?

Accepted Answer

**Solution:** 1. Given statements: - $I \geq J = K < L$ - $L > M \geq N$ - $I < O$ 2. From these, we combine the relations: - $O > I \geq J = K < L > M \geq N$ 3. Analyze each conclusion: - I. $O > L$? - We know $O > I$ and $I < L$ (since $I \geq J = K < L$), but there is no direct relation between $O$ and $L$. - So, $O > L$ is **not necessarily true**. - II. $N > L$? - Given $L > M \geq N$, so $L$ is greater than $N$. - Hence, $N > L$ is **false**. - III. $I > M$? - From $I \geq J = K < L > M$, there is no direct relation between $I$ and $M$. - So, $I > M$ is **not necessarily true**. - IV. $J < N$? - Given $J = K < L > M \geq N$, no definite relation between $J$ and $N$. - So, $J < N$ is **not necessarily true**. 4. None of the conclusions follow definitively. **Answer:** None is true.

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