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

A = {1, 2, 3, 4}
N =
2.Easy
UAB1234

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

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

Of 56 first-year students, 27 passed Mathematics (M), 24 passed Physics (P) and 30 passed Chemistry (C). 13 passed M and P, 8 passed M and C, 16 passed P and C, and 6 passed all three. How many are in none of the three sets?

|U| = 56
|(M ∪ P ∪ C)′| =
5.Hard

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

|X| = 3
N =
6.Hard

How many injective (one-to-one) functions f: A → B are there if |A| = 2 and |B| = 3? Call the number N.

|A| = 2|B| = 3
N =

Answer key

  1. 1. N = 6
  2. 2. region 4
  3. 3. reflexive
  4. 4. |(M ∪ P ∪ C)′| = 6
  5. 5. N = 216
  6. 6. N = 6

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