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

Let A = {a, b, y} and B = {1, 2, 3, 4}. Find |𝒫(𝒫(A))|.

A = {a, b, y}B = {1, 2, 3, 4}
|𝒫(𝒫(A))| =
2.Easy

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

A = {a, c, e, x}B = {1, 2}
|𝒫(A × B)| =
3.Medium
UABC12345678

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

(A ∩ C) − (B′ ∩ 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
4.Medium
ULTW

A survey of 65 people finds that 23 own a laptop (L), 25 a tablet (T) and 41 a smartwatch (W). 7 own L and T, 20 own L and W, 15 own T and W, and 6 own all three. How many are in none of the three sets?

|U| = 65
|(L ∪ T ∪ W)′| =
5.Hard

How many relations on a set with 2 elements are both reflexive and symmetric? Call the number N.

|X| = 2
N =
6.Hard
AB1234abinjective, not surjectivesurjective, not injectivebijectiveneither

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

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

Answer key

  1. 1. |𝒫(𝒫(A))| = 256
  2. 2. |𝒫(A × B)| = 256
  3. 3. region 1
  4. 4. |(L ∪ T ∪ W)′| = 12
  5. 5. N = 2
  6. 6. surjective, not injective

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