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

How many subsets of A = {1, 2, 3, 4} contain neither 4 nor 1? Call the number N.

A = {1, 2, 3, 4}
N =
2.Easy
UAB482013261419

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 = {2, 6, 14, 19, 20}B = {2, 6, 13, 14, 19}|U| = 8
|(A − B)′| =
3.Medium
UFGS

In a group of 72 students, 32 speak French (F), 36 speak German (G) and 31 speak Spanish (S). 16 speak French and German, 10 French and Spanish, 12 German and Spanish, and 5 speak all three. How many are in none of the three sets?

|U| = 72
|(F ∪ G ∪ S)′| =
4.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, 2), (1, 3), (2, 1), (2, 4), (3, 1), (3, 4), (4, 2), (4, 3)}
  1. 1reflexive
  2. 2symmetric
  3. 3antisymmetric
  4. 4transitive
5.Hard

On X = {1, 2, …, 12} the relation x ~ y holds when x ≡ y (mod 5). How many elements are in the equivalence class [5]?

X = {1, …, 12}x ~ y ⟺ 5 | (x − y)
|[5]| =
6.Hard

How many bijections f: A → B are there if |A| = |B| = 3? Call the number N.

|A| = 3|B| = 3
N =

Answer key

  1. 1. N = 4
  2. 2. |(A − B)′| = 7
  3. 3. |(F ∪ G ∪ S)′| = 6
  4. 4. symmetric
  5. 5. |[5]| = 2
  6. 6. N = 6

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