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:

Let's analyze the given statements and check each conclusion individually.

Given Statements:
1. $F=R\ge Q<P$
2. $H>Q\le J$

We can combine the relevant parts of the statements by using the common element, $Q$.

Checking Conclusion I: $H>R$
From statement 1, we have: $R\ge Q$, which means $Q\le R$.
From statement 2, we have: $H>Q$.
Combining these gives the relationship between $H$ and $R$ through $Q$:
$H>Q\le R$

Since the inequality signs between $H$ and $R$ are in opposite directions ($>$ and $\le$), no definite relationship can be established between $H$ and $R$.
Therefore, Conclusion I does not follow.

Checking Conclusion II: $J\ge F$
From statement 1, we have: $F=R\ge Q$, so $F\ge Q$, which means $Q\le F$.
From statement 2, we have: $Q\le J$.
Combining these gives the relationship between $J$ and $F$ through $Q$:
$J\ge Q\le F$

Since the inequality signs between $J$ and $F$ are in opposite directions ($\ge$ and $\le$), no definite relationship can be established between $J$ and $F$.
Therefore, Conclusion II does not follow.

Since neither Conclusion I nor Conclusion II logically follows, the correct choice is If neither conclusion I nor II is true.