# Practice Test on Sets and Subsets

In practice test on sets and subsets we will solve 15 different types of question on sets and subsets.

1. If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.

B = {2, 4}

A = {0}

C = {1, 9, 5, 13}

D = {5, 11, 1}

E = {13, 7, 9, 11, 5, 3, 1}

F = {2, 3, 4, 5}

2. Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}. Fill in the blanks by ⊂ or ⊄ to make the resulting statements true.

(a) B __ A

(b) C __ A

(c) B __ C

(d) ∅ __ B

(e) C __ C

(f) C __ B

3. Which of the following sets is a universal set for the other four sets?

(a) The set of even natural numbers

(b) The set of odd natural numbers

(c) The set of natural numbers

(d) The set of negative numbers

(e) The set of integers

4. Write all the subsets for the following.

(a) {3}

(b) {6, 11}

(c) {2, 5, 9}

(d) {1, 2, 6, 7}

(e) {a, b, c}

(f) ∅

(g) {p, q, r, s}

5. Write down all the possible proper subsets for each of the following.

(a) {a, b, c, d}

(b) {1, 2, 3}

(c) {p, q, r}

(d) {5, 10}

(e) {x}

(f) ∅

6. Find the number of subsets for set

(a) containing 3 elements

(b) whose cardinal number is 5

7. Find the number of proper subsets of a set

(a) containing 6 elements

(a) containing 6 elements

(b) whose cardinal number is 4

8. Show with an example that if the number of elements in a set is ‘n’, then

(a) the number of subsets is 2n

(b) the number of proper subsets is 2n - 1.

9. Write the universal set for the following.

(a) P = {4, 6, 8}     Q = {1, 3, 9}     R = {0, 2, 5}     S = {7}

(b) X = {a, b, c}     Y = {c, b, f}     Z = {e, g}

(c) Prime numbers less than 10, even numbers less than 10, multiples of 3 less than 10.

10. If ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {2, 4, 6, 8}

B = {3, 5, 7}

C = {1, 5, 7, 8, 9}

Find (a) A’     (b) B’     (c) C’

11. State whether true or false.

(b) {1} ↔ {0}

(c) Whole numbers ⊆ natural numbers

(d) {a} ∈ {d, e, f, a}

(e) Natural numbers ⊆ whole numbers

(f) Integers ⊆ natural numbers

(g) 0 ∈ ∅

(h) ∅ ∈ {1 , 2, 3 }

12. Let the set of integer be the universal set and let A = set of whole numbers, then what is A’?

13. Let A {x : x = n — 2, n < 5}. Find A when

(a) n = W, n ∈ W

(b) n = N, n ∈ N

(c) n ∈ I = I

14. If U = {2, 3, 4, 5, 6, 7, 8, 9}     X = {3, 5, 7, 9}     Y = {2, 4, 6, 8}

Show that X = Y’ and Y = X’

15. Let P = {3, 5, 7, 9, 11}     Q = {9, 11, 13}     R = {3, 5, 9}     S = {13, 11}

Write Yes or No for the following.

(a) R ⊂ P

(b) Q ⊂ P

(c) R ⊂ S

(d) S ⊂ Q

(e) S ⊂ P

(f) P ⊄ Q

(g) Q ⊄ R

(h) S ⊄ Q

Answers for practice test on sets and subsets are given below to check the answers of the questions.

1. C, D, E

2. (a) ⊄

(b) ⊂

(c) ⊄

(d) ⊂

(e) ⊂

(f) ⊂

3. (e)

4. (a) d, {3}

(b) d, {6}, {11}, {6, 11}

(c) d, {2}, {5}, {9}, {2, 5}, {2, 9}, {5, 9}, {2, 5, 9}

(d) d, {1}, {2}, {6}, {7}, {1, 2}, {1, 6}, {1, 7}, {2, 6}, {2, 7}, {6, 7}, {1, 2, 6}, {1, 2, 7}, {1, 6, 7}, {2, 6, 7}, {1, 2, 6, 7}

(e) {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}, d

(f) d

(g) d, {p}, {q}, {r}, {s}, {p, q}, {p, r}, {p, s}, {q, r}, {q, s}, {r, s}, {p, q, r } {p, q, s}, {p, r, s }, {q, r, s}, {p, q, r, s}

5. (a) d, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}

(b) d, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}

(c) d {p}, {q}, {r}, {p, q}, {p, r}, {q, r}

(d) d, {5}, {10}

(e) d

(f) none

6. (a) 8

(b) 32

7. (a) 63
(b) 15

9. (a) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

(b) {a, b, c, e, f, g}

(c) {2, 3, 4, 5, 6, 7, 8, 9, 10}

10. (a) {1, 3, 5, 7, 9, 10}

(b) {1, 2, 4, 6, 8, 9, 10}

(c) {2, 3, 4, 6, 10}

11. (a) True

(b) True

(c) False

(d) False

(e) True

(f) False

(g) False

(h) False

12. set of negative integers

13. (a) {0, 1, 2}

(b) {1, 2}

(c) {... -3, -2, -1, 0, 1, 2}

15. (a) Yes

(b) No

(c) No

(d) Yes

(e) No

(f) Yes

(g) Yes

(h) No

Set Theory

Sets