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 subsets of A = {1, 2, 3, 4, 5} contain neither 2 nor 3? Call the number N.

A = {1, 2, 3, 4, 5}
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
UABC12345678

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

(B ∩ A′) − (C − 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
4.Medium
UMPC

Of 42 first-year students, 14 passed Mathematics (M), 27 passed Physics (P) and 16 passed Chemistry (C). 9 passed M and P, 8 passed M and C, 10 passed P and C, and 6 passed all three. How many are in exactly one of the three sets? Call the number n.

|U| = 42
n =
5.Hard

How many surjective (onto) functions f: A → B are there if |A| = 3 and |B| = 2? Call the number N.

|A| = 3|B| = 2
N =
6.Hard
x12345f(x)53534g(x)34212

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

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

Answer key

  1. 1. N = 8
  2. 2. region 4
  3. 3. region 5
  4. 4. n = 21
  5. 5. N = 6
  6. 6. (f ∘ g)(1) = 5

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