Read the following statements carefully and the two conclusions numbered I and II that follow them. Assume the statements are true even if they contradict everyday facts, and then decide which conclusion(s) logically follow.

Statements:
F = R ≥ Q < P; H > Q ≤ J
Conclusions:
I. H > R
II. J ≥ F

The correct answer is If neither conclusion I nor II is true.

Step-by-Step Explanation:

Given Statements:

1. $F=R\ge Q<P$

2. $H>Q\le J$

Analyzing Conclusion I: $H>R$

To check the relation between $H$ and $R$, let us connect the paths involving $H$, $Q$, and $R$:

From statement 2, we have: $H>Q$

From statement 1, we have: $R\ge Q$, which means $Q\le R$

Combining these gives: $H>Q\le R$

Since the inequality signs between $H$ and $R$ face opposite directions ($>$ and $\le$), no definite relationship can be established between $H$ and $R$.

Hence, Conclusion I does not follow.

Analyzing Conclusion II: $J\ge F$

To check the relation between $J$ and $F$, let us connect the paths involving $J$, $Q$, $R$, and $F$:

From statement 2, we have: $J\ge Q$ (or $Q\le J$)

From statement 1, we have: $F=R\ge Q$, which means $Q\le R=F$

Combining these through $Q$ gives: $F=R\ge Q\le J$

Here again, the inequality signs between $F$ and $J$ face opposite directions ($\ge$ and $\le$), so no definite relationship can be established between $J$ and $F$.

Hence, Conclusion II does not follow.

Therefore, neither conclusion I nor conclusion II is true.