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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Name: ____________________   Date: ____________

1.Easy

How many proper subsets does A = {1, 2, 3, 4, 5, 6} have (subsets other than A itself)? Call the number N.

A = {1, 2, 3, 4, 5, 6}
N =
2.Easy
UAB471963917

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 = {6, 17}B = {3, 9, 17}|U| = 7
|B ∩ A| =
3.Medium
UABC1011144111182

Each number in the Venn diagram is the number of elements in that region. Find |B′ ∩ A′|.

|U| = 71
|B′ ∩ A′| =
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, 1), (1, 2), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 4)}
  1. 1reflexive
  2. 2symmetric
  3. 3antisymmetric
  4. 4transitive
5.Hard

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

|X| = 4
N =
6.Hard

How many reflexive relations are there on a set with 3 elements? Call the number N.

|X| = 3
N =

Answer key

  1. 1. N = 63
  2. 2. |B ∩ A| = 1
  3. 3. |B′ ∩ A′| = 21
  4. 4. reflexive
  5. 5. N = 65536
  6. 6. N = 64

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