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
UAB1234

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

(A ∩ B′) ∪ (B′ ∩ A)
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
2.Easy

Let A = {c, e, x} and B = {1, 2}. Find |A × B|.

A = {c, e, x}B = {1, 2}
|A × B| =
3.Medium
UFG6

In a group of 31 students, 17 speak French (F), 11 speak German (G) and 6 speak both. How many are in exactly one of the two sets?

|U| = 31|F| = 17|G| = 11|F ∩ G| = 6
|(F − G) ∪ (G − F)| =
4.Medium
UFGS

In a group of 66 students, 40 speak French (F), 38 speak German (G) and 22 speak Spanish (S). 16 speak French and German, 13 French and Spanish, 11 German and Spanish, and 3 speak all three. How many are in exactly two of the three sets? Call the number n.

|U| = 66
n =
5.Hard

On X = {1, 2, …, 14} the relation x ~ y holds when x ≡ y (mod 3). How many elements are in the equivalence class [2]?

X = {1, …, 14}x ~ y ⟺ 3 | (x − y)
|[2]| =
6.Hard

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

|X| = 4
N =

Answer key

  1. 1. region 3
  2. 2. |A × B| = 6
  3. 3. |(F − G) ∪ (G − F)| = 16
  4. 4. n = 31
  5. 5. |[2]| = 5
  6. 6. N = 11664

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