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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Name: ____________________   Date: ____________

1.Easy

How many subsets of A = {1, 2, 3, 4, 5, 6, 7} contain the element 2? Call the number N.

A = {1, 2, 3, 4, 5, 6, 7}
N =
2.Easy
UAB517192026915121618411

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

A = {2, 4, 6, 9, 11, 15}B = {4, 11, 12, 16, 18}|U| = 13
|B − A| =
3.Medium
ULTW

A survey of 27 people finds that 18 own a laptop (L), 10 a tablet (T) and 18 a smartwatch (W). 4 own L and T, 11 own L and W, 6 own T and W, and 1 own all three. How many are in L only?

|U| = 27
|L − (T ∪ W)| =
4.Medium
UABC119198982

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

|U| = 57
|A ∩ C| =
5.Hard

On X = {1, 2, …, 14} the relation x ~ y holds when x ≡ y (mod 4). How many elements are in the equivalence class [7]?

X = {1, …, 14}x ~ y ⟺ 4 | (x − y)
|[7]| =
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, a), (3, a), (4, a)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither

Answer key

  1. 1. N = 64
  2. 2. |B − A| = 3
  3. 3. |L − (T ∪ W)| = 4
  4. 4. |A ∩ C| = 11
  5. 5. |[7]| = 3
  6. 6. surjective, not injective

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