Set Operations
Union, intersection, difference and complement.
Key idea
Union, intersection, difference and complement.
In depth
Union A ∪ B (in either), intersection A ∩ B (in both), difference A \ B (in A not B), complement A′ (not in A). They obey laws like distributivity and De Morgan’s laws.
Worked example
A = {1, 2, 3}, B = {3, 4}: A ∪ B = {1, 2, 3, 4}, A ∩ B = {3}, A \ B = {1, 2}.
Formula
Real-world uses
- Finding customers who bought both products (intersection) or either product (union) in marketing
Common mistake
Confusing union with intersection.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Set Operations?
Union, intersection, difference and complement. It is a topic at the intermediate level in Discrete Math & Number Theory.
What is the formula for Set Operations?
The key formula is A∪B, A∩B, A∖B.
Where is Set Operations used in real life?
Real-world examples: Finding customers who bought both products (intersection) or either product (union) in marketing.
What should I learn before Set Operations?
Make sure you are comfortable with Subsets and Power Sets, the previous topic in Discrete Math & Number Theory.
What is a common mistake with Set Operations?
Confusing union with intersection.
How can I practise Set Operations?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Set Operations?
Move on to Venn Diagrams next.
Related intermediate topics in Discrete Math & Number Theory
- Statements and Truth Values – A proposition is true or false, never both.
- Logical Connectives – AND, OR, NOT, implication and biconditional.
- Truth Tables – List all truth assignments to evaluate compound statements.
- Subsets and Power Sets – A set with n elements has 2ⁿ subsets.
- Venn Diagrams – Pictures of sets and their overlaps.
- Cartesian Products – All ordered pairs from two sets.