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

How many subsets of A = {1, 2, 3, 4, 5, 6} contain neither 3 nor 4? Call the number N.

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

How many subsets of A = {1, 2, 3, 4, 5, 6} contain neither 5 nor 6? Call the number N.

A = {1, 2, 3, 4, 5, 6}
N =
3.Medium
ULTW

A survey of 65 people finds that 30 own a laptop (L), 39 a tablet (T) and 28 a smartwatch (W). 16 own L and T, 5 own L and W, 15 own T and W, and 2 own all three. How many are in L only?

|U| = 65
|L − (T ∪ W)| =
4.Medium
ULTW

A survey of 52 people finds that 20 own a laptop (L), 34 a tablet (T) and 22 a smartwatch (W). 13 own L and T, 10 own L and W, 14 own T and W, and 6 own all three. How many are in exactly one of the three sets? Call the number n.

|U| = 52
n =
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, a), (3, b), (4, d)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither
6.Hard

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

|X| = 2
N =

Answer key

  1. 1. N = 16
  2. 2. N = 16
  3. 3. |L − (T ∪ W)| = 11
  4. 4. n = 20
  5. 5. bijective
  6. 6. N = 4

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