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

How many subsets of A = {1, 2, 3, 4, 5, 6, 7, 8} contain the element 7? Call the number N.

A = {1, 2, 3, 4, 5, 6, 7, 8}
N =
2.Easy
UAB1234

Exactly one region of the Venn diagram is the set A′ − B′. Click its number.

A′ − B′
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
3.Medium
UABC12345678

Exactly one region of the Venn diagram is the set (C ∩ A) ∩ (A ∩ B). Click its number.

(C ∩ A) ∩ (A ∩ B)
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
  5. 5region 5
  6. 6region 6
  7. 7region 7
  8. 8region 8
4.Medium
1234

R = {(4, 1), (4, 2), (4, 3), (4, 4)} 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 reflexive?

R = {(4, 1), (4, 2), (4, 3), (4, 4)}
k =
5.Hard

How many injective (one-to-one) functions f: A → B are there if |A| = 3 and |B| = 4? Call the number N.

|A| = 3|B| = 4
N =
6.Hard

How many functions f: A → B are there if |A| = 2 and |B| = 4? Call the number N.

|A| = 2|B| = 4
N =

Answer key

  1. 1. N = 128
  2. 2. region 1
  3. 3. region 4
  4. 4. k = 3
  5. 5. N = 24
  6. 6. N = 16

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