Set theory - worksheet | PDF - Free Printable

Q1. Which of the following collections of objects are sets?
1. All planets in the solar system - Yes
2. All fast boys in the class - No
3. All dishonest businessmen in Rajkot - No
4. All children of your class who are taller than 5 feet - Yes
5. All whole numbers less than 250 - Yes

Q2. State whether the set will be a finite set or an infinite set:
1. Set of integers - Infinite
2. {x | x ∈ N, x > 1000} - Infinite
3. Set of all points on the circumference of the circle - Infinite
4. Set of all points on a line - Infinite
5. {x | x ∈ W, x < 250} - Finite

Q3. Describe the following sets in a set builder form:
1. A = {5,6,7,8,9,10} - {x | x ∈ N, 5 ≤ x ≤ 10}
2. B = {2, 3} - {x | x is a prime number and 1 < x < 4}
3. X = {44, 46, 48, 50, 52} - {x | x is an even number, 44 ≤ x ≤ 52}
4. M = { } - {x | x ≠ x} (or any contradictory condition)
5. G = {Rajkot, Jamnagar, Bhavnagar, Junagadh} - {x | x is a city in Gujarat, India}
6. H = {1, 1/2, 1/3, 1/4, 1/5} - {x | x = 1/n, n ∈ N, 1 ≤ n ≤ 5}
7. O = {Atlantic, Arctic} - {x | x is an ocean and name starts with 'A'}

Q4. Write the following sets in roster form
1. B = {x | x ∈ W, x ≤ 2} - {0, 1, 2}
2. Y = {x | x = 2n + 1, n ∈ W, n ≤ 5} - {1, 3, 5, 7, 9, 11}
3. P = {x | x is a two digit number, the sum of whose digits is 8} - {17, 26, 35, 44, 53, 62, 71, 80}
4. S = {x | x is a prime number, 5 < x < 50} - {7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}
5. I = {x | x ∈ N, x ≤ 6} - {1, 2, 3, 4, 5, 6}

Q5. Are the following sets an empty set or not?
1. A = {x | 4 < x < 5, x ∈ N} - Empty set
2. S = {0} - Not empty
3. Q = {x | x is an even prime number} - Not empty (Q = {2})
4. G = {x ∈ W, x < 2} - Not empty (G = {0, 1})

Q6. If A = {2,4,6,8,10}, B = {8,10,12}, C = {2,4,6}, find the values of:
1. A ∪ B - {2, 4, 6, 8, 10, 12}
2. A ∩ B - {8, 10}