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, c} and B = {1, 2, 3, 4}. Find |𝒫(A)|.

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

Let A = {b, x} and B = {1, 2, 3, 4}. Find |A × B|.

A = {b, x}B = {1, 2, 3, 4}
|A × B| =
3.Medium
123reflexivesymmetricantisymmetrictransitive

The relation R on {1, 2, 3} is drawn as a directed graph (a loop means (x, x) ∈ R). Exactly one of the four properties holds. Click it.

R = {(1, 1), (1, 2), (1, 3), (3, 1), (3, 2), (3, 3)}
  1. 1reflexive
  2. 2symmetric
  3. 3antisymmetric
  4. 4transitive
4.Medium
1234

R = {(1, 3), (1, 4), (2, 1), (3, 1), (3, 2), (3, 3)} is a relation on {1, 2, 3, 4}. What is the smallest number k of ordered pairs that must be added to R to make it transitive (the size of the transitive closure minus |R|)?

R = {(1, 3), (1, 4), (2, 1), (3, 1), (3, 2), (3, 3)}
k =
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, b), (3, a), (4, d)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither
6.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, b), (2, a), (3, b)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither

Answer key

  1. 1. |𝒫(A)| = 4
  2. 2. |A × B| = 8
  3. 3. transitive
  4. 4. k = 6
  5. 5. bijective
  6. 6. neither

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