Explanation:

Alright, let's get into it.

We’re supposed to switch:

- The signs ÷ and +

- The numbers 9 and 12 (not digits, so whole numbers get swapped)

Let's look at each one:

I. 12 × 2 - 72 + 9 ÷ 57 = 69

- Swapping + and ÷ gives: 12 × 2 - 72 ÷ 9 + 57

- Also swap 9 and 12: 9 × 2 - 72 ÷ 12 + 57

- Now, run through it:

9 × 2 = 18

72 ÷ 12 = 6

So: 18 - 6 + 57 = 12 + 57 = 69

- This checks out.

II. 169 + 13 × 12 ÷ 3 - 9 = 108

- Swap + and ÷: 169 ÷ 13 × 12 + 3 - 9

- Swap 9 and 12: 169 ÷ 13 × 9 + 3 - 12

- Do the math:

169 ÷ 13 = 13

13 × 9 = 117

117 + 3 - 12 = 120 - 12 = 108

- This also checks out.

Options:

- 1: Neither I nor II is incorrect.

- 2: Only II is incorrect.

- 3: Only I is incorrect.

- 4: Both I and II are incorrect.

Both statements hold up after swapping, so the correct choice is:

Option: 1. Neither I nor II