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
UAB211141914716512131868920

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

A = {1, 4, 6, 7, 8, 9, 16, 20}B = {5, 6, 8, 9, 12, 13, 18, 20}|U| = 16
|(B ∩ A)′| =
2.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 =
3.Medium
UFG14

In a group of 66 students, 44 speak French (F), 31 speak German (G) and 14 speak both. How many are in F but not in G?

|U| = 66|F| = 44|G| = 31|F ∩ G| = 14
|F − G| =
4.Medium
ULT7

A survey of 37 people finds that 17 own a laptop (L), 25 own a tablet (T) and 7 own both. How many are in exactly one of the two sets?

|U| = 37|L| = 17|T| = 25|L ∩ T| = 7
|(L − T) ∪ (T − L)| =
5.Hard
x12345f(x)41253

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

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

How many antisymmetric relations are there on a set with 2 elements? Call the number N.

|X| = 2
N =

Answer key

  1. 1. |(B ∩ A)′| = 12
  2. 2. N = 32
  3. 3. |F − G| = 30
  4. 4. |(L − T) ∪ (T − L)| = 28
  5. 5. f−1(3) = 5
  6. 6. N = 12

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