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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy

Let A = {b, c, d, x} and B = {1, 2, 3}. Find |A × B|.

A = {b, c, d, x}B = {1, 2, 3}
|A × B| =
2.Easy
UAB91910113616471220

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

A = {4, 7, 10, 11, 12, 20}B = {3, 4, 6, 7, 12, 16, 20}|U| = 11
|A ∩ B′| =
3.Medium
ULTW

A survey of 50 people finds that 21 own a laptop (L), 25 a tablet (T) and 26 a smartwatch (W). 7 own L and T, 14 own L and W, 14 own T and W, and 5 own all three. How many are in exactly two of the three sets? Call the number n.

|U| = 50
n =
4.Medium
UABC958712122

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

|U| = 46
|(A′ ∩ C) ∪ (A ∩ B)| =
5.Hard

How many different relations are there on a set with 2 elements? Call the number N.

|X| = 2
N =
6.Hard
AB1234abcdeinjective, not surjectivesurjective, not injectivebijectiveneither

The arrow diagram shows a function f: A → B with A = {1, 2, 3, 4} and B = {a, b, c, d, e}. Click the description that fits f.

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

Answer key

  1. 1. |A × B| = 12
  2. 2. |A ∩ B′| = 2
  3. 3. n = 20
  4. 4. |(A′ ∩ C) ∪ (A ∩ B)| = 23
  5. 5. N = 16
  6. 6. injective, not surjective

Full step-by-step solutions: practise this topic on examproblems.com.