This document contains 10 questions about set theory for students in grades 7 and 8. It covers topics such as identifying sets, determining if a set is finite or infinite, writing sets in roster and set-builder form, operations on sets like union and intersection, and properties of sets including equal, equivalent, and subset relationships. For example, question 1 asks students to identify which of 5 collections are sets, while question 6 has students find values of set operations like union and intersection given the sets A={2,4,6,8,10}, B={8,10,12}, C={2,4,8}, and D={10, 12}. The document aims to test students' understanding of fundamental set theory concepts.

1. SN Kansagra School
Set Theory – Work sheet
Academic Year 2012 – 2013
Std : 7 and 8 PBL Team
Q1. Which of the following collections of objects are sets?
1. All planets in the solar system
2. All fast boys in the class
3. All dishonest businessmen in Rajkot
4. All children of you class who are taller than 5 feet
5. All whole numbers less than 20
Q2. State whether the set will be a finite set or an infinite set:
1. Set of integers
2. {x | x Є N, x > 1000}
3. Set of all points on the circumference of the circle
4. Set of all points on a line
5. {x | x Є W, x < 250}
Q3. Describe the following sets in a set builder form:
1. A = {5,6,7,8,9,10}
2. B = {2, -2}
3. X = {44, 46, 48, 50, 52}
4. M = { }
5. G = { Rajkot, Jamnagar, Bhavnagar, Junagadh}
ଵ ଵ ଵ ଵ ଵ ଵ
6. R = {1, ଶ , ଷ , ସ , ହ , ଺ , ଻ }
7. O = {Atlantic, Arctic}
Q4. Write the following sets in roster form
1. B = { x | x Є W, x ≥ 7}
2. Y = { x | x = (2n + 1), n Є W, n ≤ 5}
3. T = { x | x is a two digit number , the sum of whose digits is 8}
4. S = { x | x is a prime number, 5 < x < 50 }
ଵ
5. J = { x | x = ௡ , n Є N , N < 5}
Q5. Are the following sets an empty set or not?
1. A = { x | x Є N, x + 5 = 5}
2. S = { 0 }
3. G = { x | x is an even prime number}
4. Q = { x | x Є W, x + 2 < 2 }
Q6. If A = { 2,4,6,8,10}, B = {8,10,12}, C = {2,4,8}, D = {10, 12}, find the values of:
1. ࣈ
2. A’
3. B’
4. A ∩ B
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Prepared by Kapil BHATIA – PBL Unit

2. 5. A ᴜ B
6. n (C)
7. n (D)
8. n (C ∩ D)
9. n (C ᴜ B)
10. (A ᴜ C) ‘
11. (B ∩ D) ‘
Q7. Frame two examples of Equal Sets and Equivalent Sets.
Q8. Find the power sets for Set C where C = {2,4,6}
Q9. List the elements of each of the following sets as per the set builder form.
ࣈ = {x : x Є N , x < 50}
A = { x : x2 Є ࣈ }
B = { x : x = n2, n Є N }
C = { x : x is a factor of 3}
Also state whether each of the following is true or false.
(i) A⊆B
(ii) A=B
(iii) A↔B
(iv) B↔C
(v) n(A) = n(C)
Q10. Let A = {b,c,d,e} and B = {d,e,f,g} be two subsets of the universal set ࣈ = {b,c,d,e,f,g}
Verify whether
1. (A ᴜ B) ‘ = (A’ ∩ B’)
2. (A ∩ B) ‘ = (A’ ᴜ B’)
Page 2 of 2
Prepared by Kapil BHATIA – PBL Unit