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 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

How many subsets with exactly 4 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
123

R = {(1, 3), (2, 1), (3, 1)} is a relation on {1, 2, 3}. What is the smallest number k of ordered pairs that must be added to R to make it reflexive?

R = {(1, 3), (2, 1), (3, 1)}
k =
4.Medium
UABC10105428124

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

|U| = 55
|(B − C)′| =
5.Hard

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

|X| = 4
N =
6.Hard

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

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

Answer key

  1. 1. N = 63
  2. 2. N = 70
  3. 3. k = 3
  4. 4. |(B − C)′| = 46
  5. 5. N = 64
  6. 6. N = 6

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