Counting relations and functions: Class 11 practice
If A has m elements and B has n, then A × B has mn ordered pairs, there are 2^(mn) relations from A to B, and nᵐ functions from A to B.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Sets
- Powers
The idea behind counting relations and functions
If A has m elements and B has n, then A × B has mn ordered pairs, there are 2^(mn) relations from A to B, and nᵐ functions from A to B.
Step-by-step method
- n(A × B) = mn.
- Relations = subsets of A × B = 2^(mn).
- Functions: each of the m elements picks one of n images → nᵐ.
Worked example 1 (Basic)
A has 3 elements and B has 3. How many elements are in A × B?
- 3 × 3
- Answer: 9
Worked example 2 (Standard)
How many relations are there from a 1-element set to a 3-element set?
- 2^(1 × 3)
- Answer: 8
Worked example 3 (Challenge)
How many functions are there from a 4-element set to a 2-element set?
- 2^4
- Answer: 16
Common mistakes and misconceptions
- Using mⁿ for functions
- Forgetting the empty relation
Practice questions
- (Basic) A has 2 elements and B has 2. How many elements are in A × B?
- (Basic) A has 4 elements and B has 3. How many elements are in A × B?
- (Standard) How many relations are there from a 4-element set to a 3-element set?
- (Standard) How many relations are there from a 1-element set to a 4-element set?
- (Challenge) How many functions are there from a 3-element set to a 3-element set?
- (Challenge) How many functions are there from a 1-element set to a 4-element set?
Answer key with full working
- Q1: 2 × 2 → Answer: 4
- Q2: 4 × 3 → Answer: 12
- Q3: 2^(4 × 3) → Answer: 4096
- Q4: 2^(1 × 4) → Answer: 16
- Q5: 3^3 → Answer: 27
- Q6: 4^1 → Answer: 4
Syllabus note
This skill is listed under "Relations and Functions" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is counting relations and functions in?
"Relations and Functions", Class 11 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.