Difference of Sets – Venn Diagram and Examples

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 :

difference of sets

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}.

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