Difference of set - Practice Questions & MCQ

The difference of the sets A and B in this order is the set of elements which belong to A but not to B.

Symbolically, we write A – B and read as “A minus B”.

For example, If A = {1, 2, 3, 4} and B = {4, 5, 6, 8},

Then, A - B = {1, 2, 3} and B - A = {5, 6, 8}

The sets A – B, A ∩ B and B – A are mutually disjoint sets, i.e., the intersection of any two of these sets is the null set as shown in figure

Properties of Difference of Sets

1. In general A - B does not equal B - A

2. A - A = 

3. A -  = A

4. A - U = 

5. If A is a subset of B, then A - B = 

Symmetric Difference of Sets ( A Δ B )

Symmetric difference of two sets A and B is defined as

A Δ B = ( A - B ) ∪ ( B - A )

Venn Diagram

Clearly,  A Δ B also equals ( A ∪ B) - ( A ∩ B )