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
UAB1234

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

A ∩ B
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
2.Easy

How many subsets with exactly 2 elements does A = {1, 2, 3, 4, 5, 6, 7, 8} have? Call the number N.

A = {1, 2, 3, 4, 5, 6, 7, 8}
N =
3.Medium
UMPC

Of 61 first-year students, 28 passed Mathematics (M), 41 passed Physics (P) and 27 passed Chemistry (C). 18 passed M and P, 10 passed M and C, 18 passed P and C, and 6 passed all three. How many are in exactly two of the three sets? Call the number n.

|U| = 61
n =
4.Medium
UABC12345678

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

(C′ ∩ B) ∩ (A ∪ B′)
  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

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

|A| = 5|B| = 5
N =
6.Hard

How many symmetric relations are there on a set with 4 elements? Call the number N.

|X| = 4
N =

Answer key

  1. 1. region 2
  2. 2. N = 28
  3. 3. n = 28
  4. 4. region 3
  5. 5. N = 120
  6. 6. N = 1024

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