Select the set in which the numbers are related in the same way as are the numbers of the following set.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)

(7, 1, 72)
(5, 2, 18)

Let's find the logic connecting the numbers (a,b,c) in the given sets:
For (7,1,72):

(7+1)×9=8×9=72
Or another logic:

(7
2
−1
2
)=48×1.5=72
Let's try another one:

(7+1)×(7−1)=8×6=48→not 72.
Let's check the cube/square combinations:

(a+b)×(a−b)×something?
What about (a
3
−b
3
) or (a+b) relations?
Let's look at (5,2,18):
Using the first logic: (5+2)×9=7×9=63

=18. So this is wrong.

Let's find another pattern:
For (7,1,72):

(7+1)
2
=64+8=72⟹(a+b)
2
+(a+b)=72?
Let's check for (5,2,18):

(5+2)
2
=49

=18.
Let's try:

c=(a−b)×something
For (7,1,72): 7−1=6; 72/6=12. So, (a−b)×12=72.
Let's test this with (5,2,18):
5−2=3; 18/3=6. Here it is multiplied by 6 instead of 12.
Notice that 12=2×6, and 6=2×3.
So the multiplier is 2×(a−b)?
Let's check: c=2×(a−b)
2

For (7,1,72): 2×(7−1)
2
=2×6
2
=2×36=72.
For (5,2,18): 2×(5−2)
2
=2×3
2
=2×9=18.

The logic is perfectly consistent:

c=2×(a−b)
2

Now let's check the options with this formula:

Option A: (4,2,12)→2×(4−2)
2
=2×2
2
=8

=12

Option B: (2,1,6)→2×(2−1)
2
=2×1
2
=2

=6

Option C: (7,5,45)→2×(7−5)
2
=2×2
2
=8

=45

Option D: (3,1,8)→2×(3−1)
2
=2×2
2
=2×4=8.

Option D fits the logic perfectly.