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
UAB15951219

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 = {9, 19}B = {5, 12, 19}|U| = 5
|B ∩ A| =
2.Easy
UAB1234

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

(B ∩ A) ∩ (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), (3, 1), (3, 2), (4, 2), (4, 3)}
  1. 1reflexive
  2. 2symmetric
  3. 3antisymmetric
  4. 4transitive
4.Medium
UFGS

In a group of 49 students, 24 speak French (F), 15 speak German (G) and 32 speak Spanish (S). 7 speak French and German, 13 French and Spanish, 12 German and Spanish, and 6 speak all three. How many are in none of the three sets?

|U| = 49
|(F ∪ G ∪ S)′| =
5.Hard

An equivalence relation R on {1, …, 9} has the classes {1, 7}, {2, 4, 9}, {6, 8}, {3, 5}. How many ordered pairs does R contain? Call the number |R|.

{1, 7}{2, 4, 9}{6, 8}{3, 5}
|R| =
6.Hard
x12345f(x)41235

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

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

Answer key

  1. 1. |B ∩ A| = 1
  2. 2. region 4
  3. 3. antisymmetric
  4. 4. |(F ∪ G ∪ S)′| = 4
  5. 5. |R| = 21
  6. 6. f−1(1) = 2

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