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.

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1.Easy
UAB1234

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

B ∩ A
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
2.Easy
UAB216571338101211151718

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 = {5, 7, 11, 13, 15, 17, 18}B = {3, 8, 10, 11, 12, 15, 17, 18}|U| = 13
|(B ∩ A)′| =
3.Medium
UABC12345678

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

(B ∩ C) ∩ (B ∩ A′)
  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 = {(3, 1), (3, 4), (4, 2), (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, 1), (3, 4), (4, 2), (4, 3)}
k =
5.Hard
x12345f(x)41422g(x)11155

The functions f and g on {1, 2, 3, 4, 5} are given by their tables. Find (f ∘ g)(3).

f: 1 ↦ 4, 2 ↦ 1, 3 ↦ 4, 4 ↦ 2, 5 ↦ 2g: 1 ↦ 1, 2 ↦ 1, 3 ↦ 1, 4 ↦ 5, 5 ↦ 5
(f ∘ g)(3) =
6.Hard
x12345f(x)35124

The bijection f on {1, 2, 3, 4, 5} is given by its table. Find f−1(1).

f: 1 ↦ 3, 2 ↦ 5, 3 ↦ 1, 4 ↦ 2, 5 ↦ 4
f−1(1) =

Answer key

  1. 1. region 3
  2. 2. |(B ∩ A)′| = 9
  3. 3. region 8
  4. 4. k = 2
  5. 5. (f ∘ g)(3) = 4
  6. 6. f−1(1) = 3

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