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 proper subsets does A = {1, 2, 3, 4} have (subsets other than A itself)? 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, 3), (1, 4), (2, 2), (2, 3), (3, 3), (3, 4), (4, 1), (4, 4)}
  1. 1reflexive
  2. 2symmetric
  3. 3antisymmetric
  4. 4transitive
4.Medium
ULTW

A survey of 51 people finds that 17 own a laptop (L), 28 a tablet (T) and 31 a smartwatch (W). 14 own L and T, 8 own L and W, 18 own T and W, and 6 own all three. How many are in none of the three sets?

|U| = 51
|(L ∪ T ∪ W)′| =
5.Hard
AB12abcdeinjective, not surjectivesurjective, not injectivebijectiveneither

The arrow diagram shows a function f: A → B with A = {1, 2} and B = {a, b, c, d, e}. Click the description that fits f.

f = {(1, a), (2, b)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither
6.Hard

An equivalence relation R on {1, …, 10} has the classes {3, 8}, {1, 2, 10}, {4, 5, 6}, {7, 9}. How many ordered pairs does R contain? Call the number |R|.

{3, 8}{1, 2, 10}{4, 5, 6}{7, 9}
|R| =

Answer key

  1. 1. N = 15
  2. 2. region 1
  3. 3. reflexive
  4. 4. |(L ∪ T ∪ W)′| = 9
  5. 5. injective, not surjective
  6. 6. |R| = 26

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