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
UAB1819683122010

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

A = {6, 8, 10}B = {3, 10, 12, 20}|U| = 8
|A − B| =
2.Easy

Let A = {b, c, d, x} and B = {1, 2}. Find |𝒫(𝒫(A))|.

A = {b, c, d, x}B = {1, 2}
|𝒫(𝒫(A))| =
3.Medium
UABC12345678

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

(A′ ∩ C) ∩ (B ∩ C)
  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 71 people finds that 36 own a laptop (L), 36 a tablet (T) and 22 a smartwatch (W). 14 own L and T, 12 own L and W, 11 own T and W, and 3 own all three. How many are in L only?

|U| = 71
|L − (T ∪ W)| =
5.Hard
AB1234abcdinjective, not surjectivesurjective, not injectivebijectiveneither

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

f = {(1, c), (2, d), (3, b), (4, a)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither
6.Hard
x12345f(x)35513g(x)22215

The functions f and g on {1, 2, 3, 4, 5} are given by their tables. Find (f ∘ f)(5).

f: 1 ↦ 3, 2 ↦ 5, 3 ↦ 5, 4 ↦ 1, 5 ↦ 3g: 1 ↦ 2, 2 ↦ 2, 3 ↦ 2, 4 ↦ 1, 5 ↦ 5
(f ∘ f)(5) =

Answer key

  1. 1. |A − B| = 2
  2. 2. |𝒫(𝒫(A))| = 65536
  3. 3. region 1
  4. 4. |L − (T ∪ W)| = 13
  5. 5. bijective
  6. 6. (f ∘ f)(5) = 5

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