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

How many subsets of A = {1, 2, 3, 4, 5, 6, 7} contain neither 1 nor 2? Call the number N.

A = {1, 2, 3, 4, 5, 6, 7}
N =
2.Easy

How many subsets of A = {1, 2, 3, 4, 5} contain the element 2? Call the number N.

A = {1, 2, 3, 4, 5}
N =
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
UMP10

Of 68 first-year students, 38 passed Mathematics (M), 37 passed Physics (P) and 10 passed both. How many are in M but not in P?

|U| = 68|M| = 38|P| = 37|M ∩ P| = 10
|M − P| =
5.Hard

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

|X| = 4
N =
6.Hard

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

|A| = 3|B| = 2
N =

Answer key

  1. 1. N = 32
  2. 2. N = 16
  3. 3. region 1
  4. 4. |M − P| = 28
  5. 5. N = 11664
  6. 6. N = 8

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