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
UAB472015359141018

The Venn diagram shows every element of the universal set U and of the sets A and B. Find |(A − B) ∪ (B ∩ A)|, the number of elements of (A − B) ∪ (B ∩ A).

A = {10, 15, 18}B = {3, 5, 9, 10, 14, 18}|U| = 10
|(A − B) ∪ (B ∩ A)| =
2.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 =
3.Medium
UABC1191951482

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

|U| = 59
|(C ∩ B′)′| =
4.Medium
UABC12345678

Exactly one region of the Venn diagram is the set (C ∩ B) − (A ∩ B). Click its number.

(C ∩ B) − (A ∩ B)
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
  5. 5region 5
  6. 6region 6
  7. 7region 7
  8. 8region 8
5.Hard
x12345f(x)22421g(x)33235

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

f: 1 ↦ 2, 2 ↦ 2, 3 ↦ 4, 4 ↦ 2, 5 ↦ 1g: 1 ↦ 3, 2 ↦ 3, 3 ↦ 2, 4 ↦ 3, 5 ↦ 5
(f ∘ 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, b), (3, a)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither

Answer key

  1. 1. |(A − B) ∪ (B ∩ A)| = 3
  2. 2. N = 6
  3. 3. |(C ∩ B′)′| = 40
  4. 4. region 6
  5. 5. (f ∘ f)(5) = 2
  6. 6. bijective

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