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
UAB478171015161820

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 = {7, 8, 15, 16, 17, 18, 20}B = {10, 15, 16, 18, 20}|U| = 9
|(B ∩ A)′| =
2.Easy
UAB1234

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

(A′ ∩ B) ∩ (B − A)
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
3.Medium
1234reflexivesymmetricantisymmetrictransitive

The relation R on {1, 2, 3, 4} is drawn as a directed graph (a loop means (x, x) ∈ R). Exactly one of the four properties holds. Click it.

R = {(1, 1), (2, 1), (2, 2), (3, 2), (4, 3)}
  1. 1reflexive
  2. 2symmetric
  3. 3antisymmetric
  4. 4transitive
4.Medium
UABC337586142

Each number in the Venn diagram is the number of elements in that region. Find |(B ∪ A′) − (A − C)|.

|U| = 48
|(B ∪ A′) − (A − C)| =
5.Hard
x12345f(x)34245g(x)53252

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

f: 1 ↦ 3, 2 ↦ 4, 3 ↦ 2, 4 ↦ 4, 5 ↦ 5g: 1 ↦ 5, 2 ↦ 3, 3 ↦ 2, 4 ↦ 5, 5 ↦ 2
(f ∘ f)(1) =
6.Hard
x12345f(x)24415g(x)41135

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

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

Answer key

  1. 1. |(B ∩ A)′| = 5
  2. 2. region 4
  3. 3. antisymmetric
  4. 4. |(B ∪ A′) − (A − C)| = 34
  5. 5. (f ∘ f)(1) = 2
  6. 6. (f ∘ g)(5) = 5

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