Q1. In a class of 40, 25 like tea and 20 like coffee; 10 like both. How many like at least one?
n(T∪C) = n(T) + n(C) − n(T∩C)
n(T∪C) = 25 + 20 − 10
n(T∪C) = 35
Sets — Class 11
A set is just a well-defined collection. Master union, intersection and the counting formula that unlocks most problems.
Set & subsetA well-defined collection of objects. A ⊆ B means every element of A is also in B.
Union & intersectionA ∪ B contains elements in A OR B; A ∩ B contains elements in A AND B.
ComplementA′ contains everything in the universal set that is NOT in A.
Counting formulan(A ∪ B) = n(A) + n(B) − n(A ∩ B).
Set counting calculator Interactive
Use n(A∪B) = n(A) + n(B) − n(A∩B) to find any of the four quantities.
n(A∪B)—
Only in A = n(A) − n(A∩B); only in B = n(B) − n(A∩B). This is how "how many study only Maths" questions are solved.
Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Counting (two sets) | n(A∪B) = n(A) + n(B) − n(A∩B) |
| De Morgan | (A∪B)′ = A′∩B′ |
| Subsets of a set | a set with n elements has 2ⁿ subsets |
Common mistakes & exam wins
- A set with n elements has 2ⁿ subsets (including the empty set and itself).
- Draw a Venn diagram for word problems — fill the overlap (∩) first.
- De Morgan's laws: (A∪B)′ = A′∩B′ and (A∩B)′ = A′∪B′.
Frequently asked questions
What is the formula for n(A∪B)?
n(A∪B) = n(A) + n(B) − n(A∩B).
How many subsets does a set of n elements have?
2ⁿ subsets in total.
What is the complement of a set?
All the elements of the universal set that are not in the given set.