Statements: J < Q < M = D; I < H = G ≥ D; L > O = Q

Conclusions : I. Q < H II. L > J

In these questions, the relationship between different elements is shown in the statements. The statements are followed by conclusions. Study the conclusions based on the given statements and select the appropriate answer:

Correct Answer: If both conclusions I and II are true

Step-by-Step Explanation:

Given Statements:

1. $J<Q<M=D$

2. $I<H=G\ge D$

3. $L>O=Q$

Evaluating Conclusion I: $Q<H$

To analyze the relationship between $Q$ and $H$, we combine the relevant statements that connect these elements through common terms:

From statement 1: $Q<M=D$, which gives $Q<D$.

From statement 2: $H=G\ge D$, which gives $H\ge D$, or $D\le H$.

Combining $Q<D$ and $D\le H$ gives:

$Q<D\le H$

Since the inequality signs point in the same direction, it strictly follows that $Q<H$.

Therefore, Conclusion I is true.

Evaluating Conclusion II: $L>J$

To analyze the relationship between $L$ and $J$, we connect statement 3 and statement 1 using the common element $Q$:

From statement 3: $L>O=Q$, which implies $L>Q$.

From statement 1: $J<Q$, which is equivalent to $Q>J$.

Combining $L>Q$ and $Q>J$ gives:

$L>Q>J$

Since the inequality signs point in the same direction, it strictly follows that $L>J$.

Therefore, Conclusion II is true.

Conclusion: Since both conclusions I and II are logically sound and true, the correct choice is If both conclusions I and II are true.