In each of the following questions, assuming the given statements to be true, determine which of the conclusions I, II, and III is/are definitely true. **Statements:** $B \geq D = C \leq A \geq Y$; $N \geq E M = C L \leq P$ **Conclusions:** I. $N \geq Y$ II. $B \geq M$ III. $P

Question

In each of the following questions, assuming the given statements to be true, determine which of the conclusions I, II, and III is/are definitely true.

**Statements:**

$B \geq D = C \leq A \geq Y$;

$N \geq E > M = C > L \leq P$

**Conclusions:**

I. $N \geq Y$

II. $B \geq M$

III. $P < N$

Which of the following is correct?

Accepted Answer

**Solution:** 1. From the first statement: $B \geq D = C \leq A \geq Y$ - This implies $B \geq C$ and $A \geq Y$. 2. From the second statement: $N \geq E > M = C > L \leq P$ - Here, $N \geq E$, $E > M$, and $M = C$. - Also, $C > L$ and $L \leq P$. 3. Analyze each conclusion: - **Conclusion I: $N \geq Y$** - We know $N \geq E$ and $E > M = C \leq A \geq Y$. - However, there is no direct comparison between $N$ and $Y$. - So, $N \geq Y$ cannot be confirmed definitely. - **Conclusion II: $B \geq M$** - From the first statement, $B \geq C$. - From the second, $M = C$. - Therefore, $B \geq M$ is definitely true. - **Conclusion III: $P < N$** - From the second statement, $L \leq P$ and $C > L$. - But no direct relation between $P$ and $N$ is given. - Hence, $P < N$ cannot be confirmed. **Answer:** Only conclusion II is definitely true.

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