This comprehensive practice resource on Set Theory is specially designed for B.Sc Mathematics, B.Com, BCA, and IT students who are preparing for university examinations and competitive tests. The worksheet focuses on roster form and set-builder form with a balanced mix of easy, moderate, and advanced logical reasoning problems, including infinite sets and real-world word problems. It is also highly useful for NCERT syllabus and other board classes, making it suitable for Class 11 and Class 12 students who want strong fundamentals in sets. These concepts form the foundation of Discrete Mathematics, Computer Science fundamentals, and Programming Logic, which are essential for careers in Software Development, Data Structures, Algorithms, Artificial Intelligence, and Machine Learning. For BCA and IT students, mastering sets improves understanding of Database Management Systems, Data Analytics, and Coding Interviews, while B.Com students benefit through applications in Business Mathematics and Quantitative Analysis. This high-quality practice material supports online learning, exam preparation, and career-oriented technical skills, making it valuable for students targeting high-paying tech jobs and professional growth.
Q.1
Write the set of natural numbers less than 6 in roster form.
Q.2
Write the set \(\{2,4,6,8\}\) in builder form.
Q.3
Write the set of first five whole numbers in roster form.
Q.4
Write \(\{1,4,9,16\}\) in builder form.
Q.5
Write the set of vowels in the English alphabet in roster form.
Q.6
Write the set of even natural numbers less than 10 in roster form.
Q.7
Write \(\{3,6,9,12\}\) in builder form.
Q.8
Write the set of integers between −2 and 3 in roster form.
Q.9
Write the set \(\{1,8,27\}\) in builder form.
Q.10
Write the set of consonants in the word “MATH” in roster form.
Q.11
Write the set of all even integers between 1 and 15 in roster form.
Q.12
Write \(\{5,10,15,20\}\) in builder form.
Q.13
Write the set of prime numbers less than 12 in roster form.
Q.14
Write \(\{2,3,5,7\}\) in builder form.
Q.15
Write the set of squares of natural numbers less than 6 in roster form.
Q.16
Write \(\{1,4,9,16,25\}\) in builder form.
Q.17
Write the set of multiples of 4 less than 25 in roster form.
Q.18
Write \(\{6,12,18\}\) in builder form.
Q.19
Write the set of integers satisfying \(-3 \le x \le 3\) in roster form.
Q.20
Write \(\{-2,0,2,4\}\) in builder form.
Q.21
Write the set of all natural numbers whose square is less than 30 in roster form.
Q.22
Write \(\{1,2,3,4,5\}\) in builder form using inequality.
Q.23
Write the set of all letters in the word “STATISTICS” in roster form.
Q.24
Write the set of all multiples of 7 less than 50 in roster form.
Q.25
Write \(\{7,14,21,28\}\) in builder form.
Q.26
Write the set of all odd natural numbers less than 15 in roster form.
Q.27
Write \(\{1,3,5,7,9\}\) in builder form.
Q.28
Write the set of integers whose absolute value is less than 3 in roster form.
Q.29
Write \(\{-2,-1,0,1,2\}\) in builder form.
Q.30
Write the set of all factors of 12 in roster form.
Q.31
Write \(\{1,2,3,4,6,12\}\) in builder form.
Q.32
Write the set of all multiples of 5 between 10 and 40 in roster form.
Q.33
Write \(\{10,15,20,25,30\}\) in builder form.
Q.34
Write the set of all prime numbers between 10 and 25 in roster form.
Q.35
Write \(\{11,13,17,19,23\}\) in builder form.
Q.36
Write the set of all natural numbers whose cube is less than 100 in roster form.
Q.37
Write \(\{1,2,3,4\}\) in builder form using cube condition.
Q.38
Write the set of all letters used in the word “ALGEBRA” in roster form.
Q.39
Write the set of all integers divisible by 3 and lying between −9 and 9 in roster form.
Q.40
Write \(\{-6,-3,0,3,6\}\) in builder form.
Q.41
Write the set of all even integers whose absolute value is less than or equal to 6 in roster form.
Q.42
Write \(\{-6,-4,-2,0,2,4,6\}\) in builder form.
Q.43
Write the set of all natural numbers less than 20 and divisible by 4 in roster form.
Q.44
Write \(\{4,8,12,16\}\) in builder form.
Q.45
Write the set of all integers satisfying \(x^2 \le 9\) in roster form.
Q.46
Write \(\{-3,-2,-1,0,1,2,3\}\) in builder form.
Q.47
Write the set of all natural numbers whose double is less than 15 in roster form.
Q.48
Write \(\{1,2,3,4,5,6,7\}\) in builder form.
Q.49
Write the set of all perfect squares less than 50 in roster form.
Q.50
Write \(\{1,4,9,16,25,36,49\}\) in builder form.
Q.51
Let \(A=\{x\in\mathbb{Z} : x^2-5x+6=0\}\). Write the set \(A\) in roster form.
Q.52
Write the set \(\{x\in\mathbb{N} : x \le 10 \text{ and } x \text{ is not prime}\}\) in roster form.
Q.53
If \(A=\{x : x=2n+1,\; n\in\mathbb{Z}\}\) and \(B=\{x : x=4k+1,\; k\in\mathbb{Z}\}\), write \(A\cap B\) in builder form.
Q.54
Write the set of all integers \(x\) such that \(x^2-4x+3 < 0\) in roster form.
Q.55
Let \(A=\{1,2,3,4,5\}\). Write the power set \(P(A)\) in roster form (only singleton and empty subsets).
Q.56
Write the set \(\{x\in\mathbb{Z} : |x-2|\le 3\}\) in roster form.
Q.57
Write the set of all integers whose square ends with the digit 1, less than 10, in roster form.
Q.58
Let \(U=\{1,2,3,\dots,15\}\) and \(A=\{x : x \text{ is a multiple of }3\}\). Write \(A^c\) in roster form.
Q.59
Write the set \(\{x\in\mathbb{N} : x^2 < x+20\}\) in roster form.
Q.60
Let \(A=\{x : x\in\mathbb{Z},\; x^2=4x\}\). Write \(A\) in roster form.
Q.61
Write the set of all integers \(x\) such that \(x(x-1)(x-2)=0\) in roster form.
Q.62
Write the set of all natural numbers that are both perfect squares and even, less than 50.
Q.63
If \(A=\{\text{x is odd}\;\in\mathbb{Z} : -5 < x < 5 \} \) .
Q.64
Write the set of all integers \(x\) such that \(x^2 \le 2x+8\) in roster form.
Q.65
Let \(A=\{1,2,3,4\}\). Write the set of all subsets of \(A\) having exactly two elements.
Q.66
Write the set of all integers divisible by 3 in builder form.
Q.67
Write the set \(\{x\in\mathbb{Z} : x^2 = x\}\) in roster form.
Q.68
Is the set \(\{x\in\mathbb{N} : x \text{ is even}\}\) finite or infinite? Write it in builder form.
Q.69
Write the set of all integers whose cube is an even number in builder form.
Q.70
Write the set \(\{x\in\mathbb{Z} : x^2 < 10\}\) in roster form.
Q.71
Write the set of all rational numbers between 0 and 1 in builder form.
Q.72
Is the set of all prime numbers finite or infinite? Write it in builder form.
Q.73
Let \(A=\{x\in\mathbb{Z} : |x-2|>5\}\). Express the set \(A\) in set-builder form.
Q.74
Write the set of all integers which are multiples of both 2 and 3 in builder form.
Q.75
Write the set \(\{x\in\mathbb{N} : x \text{ has exactly two distinct} \text{ factors}\}\).
Q.76
Write the set of all real numbers whose square is non-negative.
Q.77
Write the set \(\{x\in\mathbb{Z} : x^2-x \text{ is even}\}\) in builder form.
Q.78
Write the set of all natural numbers whose successor is even.
Q.79
Write the set of all integers which are neither positive nor negative.
Q.80
Write the set \(\{x\in\mathbb{Z} : x^3-x=0\}\) in roster form.
Q.81
Write the set of all irrational numbers between 1 and 2 in builder form.
Q.82
Write the set of all integers divisible by every integer.
Q.83
Write the set of all integers whose absolute value equals itself.
Q.84
Write the set \(\{x\in\mathbb{N} : x = x^2\}\) in roster form.
Q.85
Write the set of all integers which are both perfect squares and perfect cubes.
Q.86
A teacher lists all integers that leave remainder 1 when divided by 4. Write this set in builder form.
Q.87
All whole numbers whose squares are less than 50 are collected for a contest. Write the set in roster form.
Q.88
A number is chosen such that adding 3 makes it divisible by 5. Describe the set of all such integers in builder form.
Q.89
A librarian notes all page numbers that are multiples of both 4 and 6. Write the set in builder form.
Q.90
A computer program records all integers whose absolute value exceeds 10. Write this set in builder form.
Q.91
A student writes all natural numbers whose cubes end with digit 8. Write the set in builder form.
Q.92
A survey includes all real numbers whose distance from 5 is less than 2. Write this set in builder form.
Q.93
A box contains all integers whose product with the next integer is zero. Write the set in roster form.
Q.94
A game allows numbers that are perfect squares and multiples of 9. Write this set in builder form.
Q.95
A scientist records all integers whose square equals four times the number. Write the set in roster form.
Q.96
All rational numbers between 2 and 3 are collected in a database. Write this set in builder form.
Q.97
A rule selects all integers that remain unchanged when squared. Write the set in roster form.
Q.98
A machine accepts all numbers whose double is greater than or equal to their square. Write the set of integers satisfying this in roster form.
Q.99
A class lists all integers divisible by every even integer. Write the set in roster form.
Q.100
A researcher studies all integers that remain unchanged when raised to the fourth power. Write this set in roster form and comment on whether the set is finite or infinite.
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