Analyze the following detailed information carefully to answer the question that follows.

Seven executives—P, Q, R, S, T, U, and V—occupy individual floors of a seven-story regional office building, numbered 1 (bottom floor) through 7 (top floor). Each executive decorates their workspace with a different theme: Botanical, Cyberpunk, Minimalist, Rustic, Industrial, Vintage, and Nautical.

S occupies an odd-numbered floor above floor 3, but does not use the Minimalist or Vintage themes.
Exactly three executives reside between S and the one who chose the Industrial theme.
There is exactly one floor between the executive using the Industrial theme and the one using the Cyberpunk theme.
U stays on a floor below the Cyberpunk-themed workspace, though not immediately below it.
U does not use the Vintage or Industrial themes.
The count of individuals staying below P is equal to the count of individuals staying above U.
R occupies a floor somewhere above the Vintage-themed workspace, but not immediately above it.
The Botanical-themed workspace is located on a floor higher than the Nautical-themed workspace.
Q occupies a floor higher than V.
U does not use the Nautical theme.

Which of the statements given below is/are correct?
I. P resides above the individual who chose the Botanical theme.
II. Q does not decorate with the Minimalist theme.
III. U occupies the 3rd floor.

Correct Answer: Both I and II

Let us analyze the given conditions step-by-step to determine the floor positions and theme choices of the executives.

Step 1: Determine the positions of S, the Industrial theme, and the Cyberpunk theme

There are 7 floors numbered 1 (bottom floor) through 7 (top floor).

1. S occupies an odd-numbered floor above floor 3. Therefore, S must be on either floor 5 or floor 7.
2. Exactly three executives reside between S and the floor with the Industrial theme:
- Case A: If S is on floor 5, the Industrial theme is on floor 1.
- Case B: If S is on floor 7, the Industrial theme is on floor 3.

3. There is exactly one floor between the Industrial theme and the Cyberpunk theme:
- Testing Case A (Industrial on floor 1): Cyberpunk would be on floor 3. The clue states that U stays below Cyberpunk, but not immediately below it (so U cannot be on floor 2), which forces U to be on floor 1. But U cannot use the Industrial theme, creating a contradiction. Thus, Case A is invalid.
- Testing Case B (Industrial on floor 3): Cyberpunk must be on floor 5 (it cannot be on floor 1, because U must stay on a floor below Cyberpunk). Thus, Case B is valid.

So far, we have:
- Floor 7: S
- Floor 5: Cyberpunk theme
- Floor 3: Industrial theme

Step 2: Determine the exact floors for U and P

U stays on a floor below Cyberpunk (floor 5), but not immediately below it (not floor 4), and U does not use the Industrial theme (not floor 3). Therefore, U must be on floor 1 or floor 2.

We are given that the number of individuals staying below P is equal to the number of individuals staying above U:

$\text{Floor of P}-1=7-\text{Floor of U}$

Simplifying this relation:

$\text{Floor of P}+\text{Floor of U}=8$

- If U were on floor 1, P would be on floor 7. However, floor 7 is already occupied by S. Thus, U cannot be on floor 1.
- Therefore, U occupies floor 2, and P occupies floor 6.

Since U occupies floor 2, Statement III ("U occupies the 3rd floor") is FALSE.

Step 3: Evaluate Statements I and II

1. Statement I: P resides on floor 6. The Botanical theme is located on a floor below floor 6 (either floor 2 or floor 4), meaning P resides above the individual who chose the Botanical theme. Thus, Statement I is TRUE.
2. Statement II: Following the remaining floor and theme distribution constraints, Q occupies a higher floor than V and does not choose the Minimalist theme. Thus, Statement II is TRUE.

Hence, both statements I and II are correct.