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Class 11 | CBSE | MATHEMATICS
MATHEMATICS | INTERVALS OF SETS
🧠 Difference of Sets
Definition: The difference of 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".
Example 1
Let A = { 1, 2, 3, 4, 5, 6 } and B = { 2, 4, 6, 8 }.
Find A – B and B – A.
Solution:
Solution:
- A – B = { 1, 3, 5 }, since these elements belong to A but not to B.
- B – A = { 8 }, since this element belongs to B but not to A.
Example 2
Let V = { a, e, i, o, u } and B = { a, i, k, u }.
Find V – B and B – V.
Solution:
Solution:
- V – B = { e, o }, since these elements belong to V but not to B.
- B – V = { k }, since this element belongs to B but not to V.
Set-builder Notation
A – B = { x : x ∈ A and x ∉ B }
Venn Diagram – Difference of Sets
The shaded portion represents A – B.
Remark: The sets A – B, A ∩ B, and B – A are mutually disjoint, i.e., the intersection of any two of these sets is the null set (∅).