Sets, relations & functions worksheet with answers

Free printable Sets, relations & functions worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
UAB81113181461520317

The Venn diagram shows every element of the universal set U and of the sets A and B. Find |B′ ∩ A′|, the number of elements of B′ ∩ A′.

A = {3, 14, 17}B = {3, 6, 15, 17, 20}|U| = 10
|B′ ∩ A′| =
2.Easy

Let A = {a, b, d} and B = {1, 2, 3}. Find |𝒫(A × B)|.

A = {a, b, d}B = {1, 2, 3}
|𝒫(A × B)| =
3.Medium
UMPC

Of 44 first-year students, 11 passed Mathematics (M), 24 passed Physics (P) and 20 passed Chemistry (C). 4 passed M and P, 6 passed M and C, 12 passed P and C, and 3 passed all three. How many are in M only?

|U| = 44
|M − (P ∪ C)| =
4.Medium
1234

R = {(3, 3), (4, 1), (4, 3)} is a relation on {1, 2, 3, 4}. What is the smallest number k of ordered pairs that must be added to R to make it symmetric?

R = {(3, 3), (4, 1), (4, 3)}
k =
5.Hard

How many antisymmetric relations are there on a set with 4 elements? Call the number N.

|X| = 4
N =
6.Hard

How many different relations are there on a set with 3 elements? Call the number N.

|X| = 3
N =

Answer key

  1. 1. |B′ ∩ A′| = 4
  2. 2. |𝒫(A × B)| = 512
  3. 3. |M − (P ∪ C)| = 4
  4. 4. k = 2
  5. 5. N = 11664
  6. 6. N = 512

Full step-by-step solutions: practise this topic on examproblems.com.