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 its 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.)

(14, 12, 168)
(16, 13, 208)

The correct option is (19, 11, 209).

To understand why this is the correct answer, let's analyze the mathematical relationship between the numbers in the given sets:

First Set: (14, 12, 168)
If we multiply the first number by the second number, we get:

$$14\times 12=168$$

This matches the third number of the set.

Second Set: (16, 13, 208)
Applying the same operation of multiplying the first number by the second number, we get:

$$16\times 13=208$$

This also matches the third number of the set.

Thus, the logic followed by the given sets is:
First Number × Second Number = Third Number

Now, let's test the options to see which set follows this exact logic:

Option 1: (19, 11, 209)

$$19\times 11=209$$

Since the product is equal to the third number (209), this set follows the pattern.

For completeness, we can check the remaining options to verify they do not fit the pattern:
Option 2: (17, 13, 224) ⇒ $17\times 13=221$ (not 224)
Option 3: (18, 14, 262) ⇒ $18\times 14=252$ (not 262)
Option 4: (15, 14, 220) ⇒ $15\times 14=210$ (not 220)

Therefore, the set that is related in the same way is (19, 11, 209).