Worksheet on Subsets

In worksheet on subsets we will solve 10 different types of questions.

1. Which of the following are correct statements?

A = {1, 2, 3, 4, 5, 6}

(a) {2, 3} ⊂ A

(b) {1, 2, 3, 4, 5,6, 7} ⊃ A

(c) 8 ⊂ A

(d) {3, 5, 1, 7} ⊃ A

(e) {1} ⊂ A

(f) {1, 2, 3, 4} ⊂ A

(g) { } ⊃ A

(h) ϕ ⊂ A

2. How many elements are there in power set if

(a) A = {ϕ}

(b) B = {a, b}

(c) C = {l, m, n}

(d) D = {4, 9}

3. Find the number of proper subsets of the following.

(a) P = {x : x ∈ N, x < 5}

(b) Q = {x : x is an even prime number}

(c) R = {x : x ∈ W, x < 2}

(d) T = { }

(e) X = {0}

(f) Y = {x : x is prime, 2 < x < 10}

4. Write down all the subsets of

(a) {8}

(b) {p, q}

(c) {1, 3, 5}

(d) ϕ

Worksheet on Subsets
5. What universal sets would you propose for the following?

(a) The set of all squares

(b) The set of all even numbers

(c) The set of all isosceles triangles

(d) The set of all negative integers

(e) The set of all prime numbers

(f) The set of all obtuse angled triangles

6. Fill in the blank spaces using the symbols ⊂ or ⊄.

(a) {1, 2, 3} _____ {1, 3, 5}

(b) ϕ ____ {4, 7, 9}

(c) {x : x is rectangle in a plane} _____ {x : x is a quadrilateral in a plane}

(d) {x : x is an odd natural number} {x : x is an integer}

(e) {x : x is a prime number} {x : x is a composite number}

(f) {5, 10, 15, 20, 25, 30}____{10, 20, 30, 40}

7. Given set A = {a, b, c) B = {p, q, r} C = {x, y, z, m, n, t} which of following are considered as universal set for all the three sets.

(a) P = {a, b, c, p, q, x, y, m, t}

(b) Q = {ϕ}

(c) R = {a, c, q, r, b, p, t, z, m, n, x, y}

(d) S = {b, c, q, r, n, t, p, q, x, m, y, z, f, g}

8. Let A be the set of letters of the word FOLLOW. Find

(a) A

(b) n(A)

(c) Number of subsets of A

(d) Number of proper subsets of A

(e) Power set of A

9. Find the power set of the following sets.

(a) A = {a, b, c}

(b) B = {0, 7}

(c) C = {0, 5, 10}

(d) D = {x}

10. A = {x, y, z}           B = {y, p, x, q, z}

Is B ⊂ A or A ⊂ E? Give reasons.


Worksheet on Subsets Answers :


1. (a), (b), (e), (f), (h)

2. (a) 1
(b) 4
(c) 8
(d) 4

3.(a) 15
(b) 1
(c) 3
(d) 0
(e) 1
(f) 7

4. (a) ∅, {8}
(b) ∅, {p}, {q}, {p, q}
(c) ∅, {1}, {3}, {5}, {1, 3}, {1, 5}, {3, 5}, {1, 3, 5}
(d) ∅

5. (a) {quadrilaterals}
(b) N
(c) {triangles}
(d) I
(e) N
(f) {triangles}

6. (a) ⊄
(b) ⊂
(c) ⊂
(d) ⊂
(e) ⊄
(f) ⊄

7. (c)

8. (a) {F, O, L, W}
(b) 4
(c) 16
(d) 15
(e) {∅, {F}, {O}, {L}, {W}, {F, O}, {F, L}, {F, W}, {O, L}, {O, W}, {L, W}, {F, O, L}, {F, O, W}, {F, L, W}, {O, L, W}, {F, O, L, W}}


9. (a) {∅, {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b, c}}
(b) {∅, {0}, {7}, {0, 7}}
(c) {∅, {0}, {5}, {10}, {0, 5}, {0, 10}, {5, 10}, {0, 5, 10}}
(d) {∅, {x}}

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