Worksheet on Set Theory

In worksheet on set theory we will solve 10 different types of questions. The questions on sets are basically related on sets and their representation and also methods of representing a set.

1. Which of the following are well-defined sets?

(a) All the colors in the rainbow. 

(b) All the points that lie on a straight line. 

(c) All the honest members in the family. 

(d) All the consonants of the English alphabet. 

(e) All the tall boys of the school. 

(f) All the efficient doctors of the hospital. 

(g) All the hardworking teachers in a school. 

(h) All the prime numbers less than 100. 

(i) All the letters in the word GEOMETRY. 

2. Let A = (a, b, c, d, e, f}. Insert the appropriate symbol ∈ or ∉ in the blank space.

(a) d __ A

(b) y __ A

(c) m __ A

(d) a __ A

(e) e __ A

(f) x __ A

Worksheet on Set Theory
3. Write the following sets in the set builder form.

(a) A = {2, 4, 6, 8}

(b) B = {3, 9, 27, 81}

(c) C = {1, 4, 9, 16, 25}

(d) D = {1, 3, 5, ......}

(e) E = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ......., 52}

(f) F = {-10, ......, -3, -2, -1, 0, 1, 2, …..., 5}

(g) G = {O}

(h) P = { }

(i) H = {-5, 5}

(j) Q = {V, I, B, G, Y, 0, R}


4. Write the following sets in the roster form.

(a) A = {x : x ∈ W, x ≤ 5}

(b) B = {x : x ∈ I, -3 < x < 3)

(c) C = {x : x is divisible by 12}

(d) D = {x : x = 3p, p ∈ W, p ≤ 3}

(e) E = {x : x = a2, a ∈ N, 3 < a < 7}

(f) F = {x : x = n/(n + 1), n ∈ N and n ≤ 4}

(g) G = {x : x ∈ N, 3x - 2 < 5}

(h) J = {x : x ∈ N, x2 < 16}

(i) K = {x : x is a prime number which is a divisor of 42}

(j) H = {x : x is a 2-digit natural number such that the sum of its digits is 5}


5. Which of the following are the examples of an empty set?

(a) The set of even natural numbers divisible by 3.

(b) The set of all prime numbers divisible by 2.

(c) {x : x ∈ N, 5 < x < 6}

(d) The set of odd natural numbers divisible by 2.

(e) B = {O}

(f) C = { }

(g) D = {x : x ∈ R, x2 = -1}

(h) E = {x : x ∈ W, 3x + 1 = 2}

(i) P = {x : x is a prime number, 54 < x < 58}

(j) Q = {x : x = 2n + 3, n ∈ W, n ≤ 5}

Worksheet on Set Theory
6. Classify the following as finite and infinite sets.

(a) The set of days in a week

(b) A = {x : x ∈ N x > 1}

(c) B = {x : x is an even prime number}

(d) C = {x : x is a multiple of 5}

(e) D = {x : x is a factor of 30}

(f) P = {x : x ∈ Z, x < -1}

(g) The set of all letters in the English alphabet

(h) The set of all real numbers


7. From the sets given below, identify the equal sets.

A = {3, 5, 9, 11}         Q = {m, s, t} 

B = {8, 9, 1, 13}         R = {o, p, a, z} 

C = {-3, 3}           T = {1, 8, 9, 13}

D = {s, t, m}           M = {3, -3} 

P = {9, 3, 5, 11} 

X = {a, o, z, p}


8. Are the following pairs of sets equal?

(a) A = {2}           B = {x : x ∈ N, x is an even prime number}.

(b) P = {1, 4, 9}         Q = {x : x = n2, n ∈ N, n ≤ 3) 

(c) X = {x : x ∈ W, x < 5}       Y = {x : x ∈ N, x ≤ 5} 

(d) M = {a, b, c, d}         N = {p, q, r, s}

(e) D = {x : x is a multiple of 30}     E = {x : x is a factor of 10}



Worksheet on Set Theory
9. Which of the following are equivalent sets?

(a) A = {1, 2, 3}           B = {4, 5} 

(b) P = {q, s, m}           Q = {6, 9, 12} 

(c) X = {x : x is a prime number less than 10}       Y = {x : x ∈ N, x ≤ 4}

(d) R = {x : x = 2n + 3, n < 4, n ∈ N}      S = {x : x = n/(n + 1), n ∈ R, n ≤ 4} 

(e) The set of vowels in the English alphabet 

(f) The set of consonants in the English alphabet


10. Find the cardinal number of the following sets.

(a) A = {x : x ∈ I, 2 < x < 7} 

(b) B = {x : n ∈ N, x = n2, n < 3}

(c) The set of months in a year 

(d) C = {x : x ∈ Z+, x < 100}

(e) D = {x : x = n3, n ∈ W, n < 5} 

(f) The set of letters in the word MALAYALAM


Answers for worksheet on set theory are given below to make sure that the answers are correct.


Answers:


1. (a), (b), (d), (h), (i) 

2. (a) ∈

(b) ∉

(c) ∉

(d) ∈

(e) ∈

(f) ∉

3. (a) {x : x is even and x ≤ 8}

(b) {x : x = 3n, n ∈ N, n ≤ 4}

(c) {x : x = n2, n ≤ 5, n ∈ N}

(d) {x : x is odd}

(e) {x : x is even, 4 ≤ x ≤ 52 and y : y = 3(2m + 1), 1 ≤ m ≤ 8}

(f)

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