Explanation:

Let's analyze the original sets:

- (7, 3, 43):

7² - 3² = 49 - 9 = 40 ? 43

7 * 3 + 22 = 21 + 22 = 43

- (5, 2, 21):

5² - 2² = 25 - 4 = 21

The relationships in the original sets are different—first is multiplication and adding 22, while second is difference of squares.

Let’s check the options:

- Option 1: (11, 5, 111):

11 * 5 = 55, 55 + 56 = 111 (fixing the same "+22" from first pair, the digits don't align).

11² - 5² = 121 - 25 = 96

No clear similarity.

- Option 2: (15, 6, 34):

15 * 6 = 90, 90 + 22 = 112

15² - 6² = 225 - 36 = 189

No match.

- Option 3: (13, 23, 131):

13 * 23 = 299

13² - 23² = 169 - 529 = -360

No match.

- Option 4: (12, 3, 43):

12 * 3 = 36

12² - 3² = 144 - 9 = 135

36 + 7 = 43

In the first pair, 7 * 3 + 22 = 43; here, 12 * 3 + 7 = 43 (pattern is directly relating via multiplication plus a fixed number). The pattern here is closest to the first in the original.

Summary:

- The first original pair uses multiplication plus a fixed number, the second uses difference of squares. Of all options, Option 4 is the closest, mirroring the "multiplication plus a fixed value" operation.

Correct Answer:

Option 4: (12, 3, 43)

Explanation:

- Option 1 does not match multiplication-plus-addition or difference-of-squares.

- Option 2 and 3 do not match either pattern.

- Option 4, (12, 3, 43), best matches the "multiplication plus a value" pattern seen in the first original set.