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
UAB2111671

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 = {1, 11, 16}B = {1, 7}|U| = 5
|(A′ ∪ B′) ∪ (B′ ∩ A)| =
2.Easy

Let A = {b, x, y} and B = {1, 2, 3, 4}. Find |𝒫(𝒫(A))|.

A = {b, x, y}B = {1, 2, 3, 4}
|𝒫(𝒫(A))| =
3.Medium
ULTW

A survey of 53 people finds that 26 own a laptop (L), 27 a tablet (T) and 27 a smartwatch (W). 15 own L and T, 12 own L and W, 12 own T and W, and 6 own all three. How many are in L only?

|U| = 53
|L − (T ∪ W)| =
4.Medium
UABC12345678

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

(C′ − A) ∩ (B′ − A)
  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)32443g(x)41514

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

f: 1 ↦ 3, 2 ↦ 2, 3 ↦ 4, 4 ↦ 4, 5 ↦ 3g: 1 ↦ 4, 2 ↦ 1, 3 ↦ 5, 4 ↦ 1, 5 ↦ 4
(f ∘ g)(1) =
6.Hard
x12345f(x)32544g(x)43123

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

f: 1 ↦ 3, 2 ↦ 2, 3 ↦ 5, 4 ↦ 4, 5 ↦ 4g: 1 ↦ 4, 2 ↦ 3, 3 ↦ 1, 4 ↦ 2, 5 ↦ 3
(f ∘ g)(3) =

Answer key

  1. 1. |(A′ ∪ B′) ∪ (B′ ∩ A)| = 4
  2. 2. |𝒫(𝒫(A))| = 256
  3. 3. |L − (T ∪ W)| = 5
  4. 4. region 6
  5. 5. (f ∘ g)(1) = 4
  6. 6. (f ∘ g)(3) = 3

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