Question

If A, B, C, D are the different sets as given below
A= {3,6,12,15,18,21}, B= {4,8,12,16,20}, C= {2,4,6,8,10,12,14,16} and D= {5,10,15,20}
Find: A-D

Answer 1

Hint: Proceed the solution by using the condition that the difference of two sets, written A - B is the set of all elements of A that are not elements of B.

Complete step-by-step answer:
In order to solve this problem, let us take a simple example of subtraction, which is 5 - 2 = 3. It would be demonstrated by starting with five objects, removing two of them and then counting it will remain 3.
As we find the difference between two numbers, in a similar way, we can find the difference of two sets.

In our question it is given that the sets A= {3,6,12,15,18,21} and D = {5,10,15,20}.
To find the difference A - D of these two sets, we can begin by writing all of the elements of A, and then take away every element of A that is also present in set D. Since A shares only elements 15 with D, this gives us the set difference A - D = {3,6,12,18,21}.

Note: Whenever we come up with such types of questions we should remember that just as the differences 4 - 7 and 7 - 4 give us different answers, similarly we need to be careful about the order in which we compute the set difference. In other words, we can say the set operation of difference is not commutative. We can more precisely state that for all sets A and B, A - B is not equal to B - A.