Given the statements: - $L I = N P$ - $I \geq R K$ - $N \leq E P$ II. $R

Question

Given the statements: - $L > I = N > P$ - $I \geq R > K$ - $N \leq E < Z$ Determine the truth of the following conclusions: I. $E > P$ II. $R < L$ Choose the correct option based on the conclusions.

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**Solution:** 1. From the first statement, we have: - $L > I = N > P$ This means $L$ is greater than $I$ and $N$, and both $I$ and $N$ are equal and greater than $P$. 2. From the second statement: - $I \geq R > K$ This implies $I$ is greater than or equal to $R$, and $R$ is greater than $K$. 3. From the third statement: - $N \leq E < Z$ This tells us $E$ is greater than or equal to $N$, and $E$ is less than $Z$. **Analyzing Conclusion I: $E > P$** - Since $E \geq N$ and $N > P$, by transitive relation, $E > P$. - Therefore, conclusion I is true. **Analyzing Conclusion II: $R < L$** - From the first statement, $L > I$. - From the second statement, $I \geq R$. - Combining these, $L > I \geq R$ implies $L > R$, or $R < L$. - Hence, conclusion II is also true. Since both conclusions I and II are true, the correct answer is option (e). **Answer:** (e) Both conclusions I and II are true.

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