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
UAB61517122012101914

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

A = {12, 14, 20}B = {1, 2, 10, 14, 19}|U| = 10
|A′ ∪ B| =
2.Easy

How many subsets with exactly 2 elements does A = {1, 2, 3, 4, 5} have? Call the number N.

A = {1, 2, 3, 4, 5}
N =
3.Medium
UABC101211105114

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

|U| = 54
|(C ∪ B′) − (C ∪ B)| =
4.Medium
UFGS

In a group of 60 students, 33 speak French (F), 30 speak German (G) and 22 speak Spanish (S). 18 speak French and German, 6 French and Spanish, 9 German and Spanish, and 4 speak all three. How many are in F only?

|U| = 60
|F − (G ∪ S)| =
5.Hard
x12345f(x)43223g(x)22542

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

f: 1 ↦ 4, 2 ↦ 3, 3 ↦ 2, 4 ↦ 2, 5 ↦ 3g: 1 ↦ 2, 2 ↦ 2, 3 ↦ 5, 4 ↦ 4, 5 ↦ 2
(g ∘ f)(5) =
6.Hard
x12345f(x)15234

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

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

Answer key

  1. 1. |A′ ∪ B| = 8
  2. 2. N = 10
  3. 3. |(C ∪ B′) − (C ∪ B)| = 11
  4. 4. |F − (G ∪ S)| = 13
  5. 5. (g ∘ f)(5) = 5
  6. 6. f−1(5) = 2

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