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
UAB121735191013

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 = {3, 5, 13, 19}B = {10, 13}|U| = 8
|B − A| =
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
123reflexivesymmetricantisymmetrictransitive

The relation R on {1, 2, 3} is drawn as a directed graph (a loop means (x, x) ∈ R). Exactly one of the four properties holds. Click it.

R = {(1, 3), (3, 1), (3, 3)}
  1. 1reflexive
  2. 2symmetric
  3. 3antisymmetric
  4. 4transitive
4.Medium
UABC1012131071083

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

|U| = 73
|(B ∩ A) − (B′ ∩ C)| =
5.Hard
x12345f(x)33142g(x)23144

The functions f and g on {1, 2, 3, 4, 5} are given by their tables. Find (g ∘ f)(5).

f: 1 ↦ 3, 2 ↦ 3, 3 ↦ 1, 4 ↦ 4, 5 ↦ 2g: 1 ↦ 2, 2 ↦ 3, 3 ↦ 1, 4 ↦ 4, 5 ↦ 4
(g ∘ f)(5) =
6.Hard
AB123abcinjective, not surjectivesurjective, not injectivebijectiveneither

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

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

Answer key

  1. 1. |B − A| = 1
  2. 2. region 4
  3. 3. symmetric
  4. 4. |(B ∩ A) − (B′ ∩ C)| = 13
  5. 5. (g ∘ f)(5) = 3
  6. 6. neither

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