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
UAB1351915

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

A = {3, 5, 15}B = {15, 19}|U| = 5
|(B′ ∩ A) ∪ (B ∩ A′)| =
2.Easy

Let A = {d, e, x, y} and B = {1, 2, 3, 4}. Find |A × B|.

A = {d, e, x, y}B = {1, 2, 3, 4}
|A × B| =
3.Medium
1234

R = {(1, 1), (3, 4), (4, 1), (4, 3), (4, 4)} is a relation on {1, 2, 3, 4}. What is the smallest number k of ordered pairs that must be added to R to make it symmetric?

R = {(1, 1), (3, 4), (4, 1), (4, 3), (4, 4)}
k =
4.Medium
ULTW

A survey of 55 people finds that 25 own a laptop (L), 26 a tablet (T) and 29 a smartwatch (W). 5 own L and T, 11 own L and W, 13 own T and W, and 1 own all three. How many are in none of the three sets?

|U| = 55
|(L ∪ T ∪ W)′| =
5.Hard
x12345f(x)54125g(x)21255

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

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

How many relations on a set with 3 elements are both reflexive and symmetric? Call the number N.

|X| = 3
N =

Answer key

  1. 1. |(B′ ∩ A) ∪ (B ∩ A′)| = 3
  2. 2. |A × B| = 16
  3. 3. k = 1
  4. 4. |(L ∪ T ∪ W)′| = 3
  5. 5. (g ∘ f)(4) = 1
  6. 6. N = 8

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