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
UAB687151115101419

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

A = {7, 10, 14, 19}B = {1, 5, 10, 11, 14, 15, 19}|U| = 10
|(A′ − B′) ∪ (B ∩ A′)| =
2.Easy

Let A = {b, x, y} and B = {1, 2}. Find |𝒫(A × B)|.

A = {b, x, y}B = {1, 2}
|𝒫(A × B)| =
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, 2), (2, 3), (3, 3), (3, 4), (4, 3), (4, 4)}
  1. 1reflexive
  2. 2symmetric
  3. 3antisymmetric
  4. 4transitive
4.Medium
UABC12345678

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

(A′ − C′) ∩ (B′ ∩ C)
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
  5. 5region 5
  6. 6region 6
  7. 7region 7
  8. 8region 8
5.Hard
x12345f(x)32153g(x)31223

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

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

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

|X| = 4
N =

Answer key

  1. 1. |(A′ − B′) ∪ (B ∩ A′)| = 4
  2. 2. |𝒫(A × B)| = 64
  3. 3. reflexive
  4. 4. region 4
  5. 5. (g ∘ f)(2) = 1
  6. 6. N = 4096

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