01 Key Concepts
Set Notation
A set is written with curly braces, like A = {1,2,3}. An element x belonging to set A is written 'x is in A'.
Subset
Set A is a subset of B if every element of A is also in B, written 'A is a subset of B'.
Union (A union B)
The set containing every element that is in A, in B, or in both.
Intersection (A intersection B)
The set containing only the elements that are in both A and B.
Complement and Empty Set
The complement of A contains everything in the universal set that is NOT in A. The empty set (written as {} or the empty-set symbol) contains no elements at all.
Cardinality
The number of elements in a set, written |A|.
02 Key Formulas
- |A union B| = |A| + |B| - |A intersection B|
03 Solved Examples
Example 1 Let A = {1,2,3,4} and B = {3,4,5,6}. Find A union B.
- Combine every element from both sets, listing duplicates only once.
- A union B = {1,2,3,4,5,6}.
Answer: A union B = {1,2,3,4,5,6}
Example 2 Using the same sets, find A intersection B.
- Find elements that appear in both A and B.
- 3 and 4 are in both sets.
Answer: A intersection B = {3,4}
Example 3 Using |A|=4, |B|=4, |A intersection B|=2, find |A union B|.
- Apply the formula: |A union B| = |A| + |B| - |A intersection B| = 4+4-2.
Answer: |A union B| = 6
04 Practice Questions
1Let A={1,2,3}, B={2,3,4}. Find A union B.
{1,2,3,4}
2Let A={1,2,3}, B={2,3,4}. Find A intersection B.
{2,3}
3Is {1,2} a subset of {1,2,3}?
Yes
4Find |A| if A = {5,10,15,20}.
4
5What is the empty set?
A set containing no elements
📄 Sets — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.