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, d} and B = {1, 2}. Find |𝒫(A)|.

A = {a, b, d}B = {1, 2}

|𝒫(A)| =

2.Easy

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 = {10, 12, 13, 18}B = {6, 10, 13, 17, 18, 19, 20}|U| = 9

|(B ∪ A)′| =

3.Medium

R = {(1, 3), (2, 1), (2, 3), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2)} 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 symmetric?

R = {(1, 3), (2, 1), (2, 3), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2)}

k =

4.Medium

Of 65 first-year students, 36 passed Mathematics (M), 38 passed Physics (P) and 13 passed both. How many are in at least one of the two sets?

|U| = 65|M| = 36|P| = 38|M ∩ P| = 13

|M ∪ P| =

5.Hard

How many injective (one-to-one) functions f: A → B are there if |A| = 5 and |B| = 6? Call the number N.

|A| = 5|B| = 6

N =

6.Hard

How many reflexive relations are there on a set with 4 elements? Call the number N.

|X| = 4

N =

Answer key

1. |𝒫(A)| = 8
2. |(B ∪ A)′| = 1
3. k = 4
4. |M ∪ P| = 61
5. N = 720
6. N = 4096

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