Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting /multiplying, etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(13,22,2)
(4,26,15)

The correct option is (23, 43, 13).

To find the correct set, let us analyze the mathematical relationship between the numbers in the given sets:
Let the numbers in each set be represented as ($A$, $B$, $C$).

By observing the given sets, we can establish the following pattern:
$$B=A+C+7$$
In other words, the second number is obtained by adding the first and third numbers together, and then adding $7$ to the sum.

Let us verify this logic with the given sets:

First Set: (13, 22, 2)
Here, $A=13$ and $C=2$.
Applying the pattern:
$$B=13+2+7=22$$
This matches the second number of the set.

Second Set: (4, 26, 15)
Here, $A=4$ and $C=15$.
Applying the pattern:
$$B=4+15+7=26$$
This matches the second number of the set.

Now, let us test the options to find the one that follows the same logic:

Option 1: (23, 43, 13)
Here, $A=23$ and $C=13$.
Applying the pattern:
$$B=23+13+7=43$$
Since $43$ matches the second number in the set, this option follows the same logic.