Consider the following statements:
I. If A ≤ B > C < D > E > F ≥ G = H; then B is always greater than E.
II. If P > Q = R ≥ S = T ≤ U = V > W; then S is always less than V.
Which of the statements given above is/are correct?

The correct answer is Neither I nor II.

Step-by-Step Analysis:

Analysis of Statement I:

The given relation is:

$A\le B>C<D>E>F\ge G=H$

We need to check the relationship between B and E.

Looking at the path from B to E: $B>C<D>E$

Notice the signs between B and D: we have a greater-than sign ($>$) followed by a less-than sign ($<$). When opposite inequality symbols appear between two variables, no definite relationship can be established between them.

Therefore, B is not necessarily greater than E. Thus, Statement I is incorrect.

Analysis of Statement II:

The given relation is:

$P>Q=R\ge S=T\le U=V>W$

We need to check the relationship between S and V.

Looking at the path from S to V: $S=T\le U=V$

Combining these equalities and inequalities gives: $S\le V$

This means S can be less than V or S can be equal to V ($S\le V$). Therefore, S is not always strictly less than V, as the possibility of $S=V$

Since both statements are incorrect, the correct choice is Neither I nor II.