Question

If A,B are any two non-empty sets, is A – B = B – A? ​

Answer 1

QuestioN :

• A, B are two non-empty sets.

To FinD :

• A - B = B - A or A - B ≠ B - A

AnsweR :

We are given A and B are two non - empty sets. And the sets A - B is not equal to B - A in every case. Because the elements of Set - A, not might be equal to elements of Set-B.

Cases Where This is Satisfied :

If all the elements of Set A as well as Set B are equal then it would be Satisfied, means A-B will be equal to B-A

And there is one more case in which the Condition A - B = B - A can be satisfied. If they will be empty sets.

$\rule{150}{0.5}$

Additional information :

• The sets which contains same elements are known as equal sets. example : A = {1,2,3} and B = {1,2,3}

• Empty sets are those sets which don't contain any element except $\phi$ (phi), which also means null value.

Answer 2

Answer: Not Necessarily

Step - by - step explanation: A - B or B - A simply means removing intersection plane from complete unit.

As you can see in the image I attached, if I want to get only A from set A then A - B will be whole set A - intersection. Similarly, for only B will need to get B - A i.e., B - intersection.

Since in both cases we have to subtract intersection hence it depends on how many & what kind of elements set A and set B have. If they are same (equal) then A - B = B - A else A - B ≠ B - A.

Regards