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} contain neither 4 nor 5? Call the number N.

A = {1, 2, 3, 4, 5}
N =
2.Easy
UAB1431112131582021618

The Venn diagram shows every element of the universal set U and of the sets A and B. Find |A ∩ B|, the number of elements of A ∩ B.

A = {2, 3, 11, 12, 13, 16, 18}B = {1, 2, 5, 8, 16, 18, 20}|U| = 12
|A ∩ B| =
3.Medium
1234

R = {(1, 3), (2, 1), (2, 4), (3, 1), (4, 1), (4, 4)} is a relation on {1, 2, 3, 4}. What is the smallest number k of ordered pairs that must be added to R to make it transitive (the size of the transitive closure minus |R|)?

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

Of 64 first-year students, 17 passed Mathematics (M), 31 passed Physics (P) and 35 passed Chemistry (C). 6 passed M and P, 9 passed M and C, 19 passed P and C, and 5 passed all three. How many are in M only?

|U| = 64
|M − (P ∪ C)| =
5.Hard
AB1234abcdinjective, not surjectivesurjective, not injectivebijectiveneither

The arrow diagram shows a function f: A → B with A = {1, 2, 3, 4} and B = {a, b, c, d}. Click the description that fits f.

f = {(1, d), (2, b), (3, c), (4, a)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither
6.Hard
x12345f(x)23154

The bijection f on {1, 2, 3, 4, 5} is given by its table. Find f−1(1).

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

Answer key

  1. 1. N = 8
  2. 2. |A ∩ B| = 3
  3. 3. k = 4
  4. 4. |M − (P ∪ C)| = 7
  5. 5. bijective
  6. 6. f−1(1) = 3

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