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 (B′ ∩ A) ∩ (A ∩ B′). Click its number.

(B′ ∩ A) ∩ (A ∩ B′)
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
2.Easy
UAB1234

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

B ∩ A′
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
3.Medium
UFG11

In a group of 60 students, 35 speak French (F), 28 speak German (G) and 11 speak both. How many are in F but not in G?

|U| = 60|F| = 35|G| = 28|F ∩ G| = 11
|F − G| =
4.Medium
UFGS

In a group of 41 students, 15 speak French (F), 14 speak German (G) and 26 speak Spanish (S). 5 speak French and German, 11 French and Spanish, 7 German and Spanish, and 2 speak all three. How many are in exactly one of the three sets? Call the number n.

|U| = 41
n =
5.Hard

On X = {1, 2, …, 10} the relation x ~ y holds when x ≡ y (mod 2). How many elements are in the equivalence class [2]?

X = {1, …, 10}x ~ y ⟺ 2 | (x − y)
|[2]| =
6.Hard
AB123abcdinjective, not surjectivesurjective, not injectivebijectiveneither

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

f = {(1, c), (2, b), (3, c)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither

Answer key

  1. 1. region 3
  2. 2. region 3
  3. 3. |F − G| = 24
  4. 4. n = 15
  5. 5. |[2]| = 5
  6. 6. neither

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