Set Theory & Venn Diagrams explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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A set is a collection of objects.
Set theory gives a clear way to group numbers, people, objects, or outcomes.
It is used in logic, probability, functions, data, and Venn diagrams.
A set is usually written with braces, such as A = {1, 2, 3}.
Each object inside a set is called an element.
A subset is a set whose elements are all inside another set.
The union of two sets contains everything in either set.
The intersection of two sets contains only the elements common to both sets.
A Venn diagram shows these relationships using circles.
Meaning: A set is a collection. An element is a member of that collection.
Definition: If 3 belongs to A, we write 3 in A.
For A = {2, 4, 6}, the number 4 is an element of A.
Meaning: A subset is fully inside another set.
Definition: A is a subset of B if every element of A is also in B.
If A = {1, 2} and B = {1, 2, 3}, then A is a subset of B.
Meaning: Union means all elements in either set.
Definition: A union B contains elements in A or B or both.
If A = {1, 2} and B = {2, 3}, then A union B = {1, 2, 3}.
Meaning: Intersection means common elements.
Definition: A intersection B contains elements that are in both A and B.
If A = {1, 2} and B = {2, 3}, then A intersection B = {2}.
Easy
Question: If A = {1, 3, 5} and B = {3, 5, 7}, find A intersection B.
Medium
Question: In a class, 18 students like cricket, 12 like football, and 5 like both. How many like cricket or football?
Exam-level
Question: If , , and , find n(A intersection B).
Counting the overlap twice
Why it happens: Both set totals include the common part.
Correct approach: Subtract the intersection once.
Confusing union and intersection
Why it happens: The words are similar at first.
Correct approach: Union means all. Intersection means common.
Ignoring elements outside both sets
Why it happens: Only the circles are counted.
Correct approach: Check whether the question asks about the universal set.
What does a Venn diagram show?
It shows how sets overlap or stay separate.
What is the difference between union and intersection?
Union includes all elements from either set. Intersection includes only common elements.
Why do we subtract the overlap?
Because it was counted once in each set total.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.