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

Let A = {b, c, y} and B = {1, 2, 3}. Find |𝒫(A)|.

A = {b, c, y}B = {1, 2, 3}
|𝒫(A)| =
2.Easy
UAB21414111281715

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 = {1, 4, 11, 12, 15}B = {8, 15, 17}|U| = 9
|B′ ∩ A| =
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, 3), (1, 4), (2, 2), (3, 1), (3, 3), (4, 1), (4, 4)}
  1. 1reflexive
  2. 2symmetric
  3. 3antisymmetric
  4. 4transitive
4.Medium
UABC34912713146

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

|U| = 68
|A ∩ C| =
5.Hard

How many surjective (onto) functions f: A → B are there if |A| = 5 and |B| = 2? Call the number N.

|A| = 5|B| = 2
N =
6.Hard
AB123abcdeinjective, not surjectivesurjective, not injectivebijectiveneither

The arrow diagram shows a function f: A → B with A = {1, 2, 3} and B = {a, b, c, d, e}. Click the description that fits f.

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

Answer key

  1. 1. |𝒫(A)| = 8
  2. 2. |B′ ∩ A| = 4
  3. 3. symmetric
  4. 4. |A ∩ C| = 19
  5. 5. N = 30
  6. 6. injective, not surjective

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