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′. Click its number.

A′ ∩ B′
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
2.Easy
UAB114187101541617193

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

A = {3, 7, 10, 15}B = {3, 4, 16, 17, 19}|U| = 11
|(B ∩ A) ∩ (A ∩ B)| =
3.Medium
UABC213113146

Each number in the Venn diagram is the number of elements in that region. Find |B ∩ A|.

|U| = 31
|B ∩ A| =
4.Medium
UABC12345678

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

(B′ − C) ∩ (C ∪ A)
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
  5. 5region 5
  6. 6region 6
  7. 7region 7
  8. 8region 8
5.Hard
AB123abcinjective, not surjectivesurjective, not injectivebijectiveneither

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

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

How many bijections f: A → B are there if |A| = |B| = 6? Call the number N.

|A| = 6|B| = 6
N =

Answer key

  1. 1. region 2
  2. 2. |(B ∩ A) ∩ (A ∩ B)| = 1
  3. 3. |B ∩ A| = 7
  4. 4. region 8
  5. 5. neither
  6. 6. N = 720

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