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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Name: ____________________   Date: ____________

1.Easy

How many proper subsets does A = {1, 2, 3, 4, 5, 6} have (subsets other than A itself)? Call the number N.

A = {1, 2, 3, 4, 5, 6}
N =
2.Easy
UAB1234

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

B′ ∩ A′
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
3.Medium
UMP5

Of 45 first-year students, 27 passed Mathematics (M), 22 passed Physics (P) and 5 passed both. How many are in M but not in P?

|U| = 45|M| = 27|P| = 22|M ∩ P| = 5
|M − P| =
4.Medium
UFGS

In a group of 56 students, 33 speak French (F), 26 speak German (G) and 21 speak Spanish (S). 12 speak French and German, 14 French and Spanish, 9 German and Spanish, and 5 speak all three. How many are in exactly one of the three sets? Call the number n.

|U| = 56
n =
5.Hard

How many functions f: A → B are there if |A| = 2 and |B| = 5? Call the number N.

|A| = 2|B| = 5
N =
6.Hard
x12345f(x)24452g(x)25352

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

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

Answer key

  1. 1. N = 63
  2. 2. region 2
  3. 3. |M − P| = 22
  4. 4. n = 25
  5. 5. N = 25
  6. 6. (f ∘ g)(4) = 2

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