Here you will learn what is the difference of two sets with venn diagram and examples.
Let’s begin –
What is Difference of Two Sets ?
Definition : Let A and B be two sets. The difference of A and B, written as A – B, is the set of all those elements of A which do not belong to B.
Thus, A – B = {x : x \(\in\) A and x \(\in\) B}
or, A – B = {x \(\in\) A : x \(\notin\) B}.
Clearly, x \(\in\) A – B \(iff\) x \(\in\) A and x \(\notin\) B.
Similarly, the difference B – A is the set of all those elements of B that do not belong to A i.e.
B – A = {x \(\in\) B : x \(\notin\) A}
In the diagram given below, the coloured part shows A – B and B – A, which is the difference of two set.
Also Read : Formulas and Operation of Sets
Venn Diagram :
Example : If A = {2, 3, 4, 5, 6, 7} and B = {3, 5, 7, 9, 11, 13}, then find the difference A – B and B – A.
Solution : We have sets A and B.
Then, A – B = {2, 4, 6}
And B – A = {9, 11, 13}.
