**Sets Worksheet –
ICSE – Class 8**
**Instructions:**
1. Answer all the questions.
2. Circle or underline your final answer.
3. Show your work or reasoning if required.
4. Answers to all the problems are given at the end. You
should look at the solutions only after attempting all the problems.
**Questions:**
1. Define a "set" in your own words. Provide an
example.
2. Classify the following into sets:
a) The days of the
week
b) Even numbers
less than 20
c) Vowels in the
English alphabet
3. List the elements of the set A = {2, 4, 6, 8, 10}. Also,
find the cardinality of set A.
4. Create a set B with the first five prime numbers. Write
it in the set-builder notation.
5. Determine whether the following statements are true or
false:
a) {1, 2, 3} ⊆
{1, 2, 3, 4, 5}
b) {a, b, c} ⊇
{b, c, d}
c) {2, 4, 6} ⊂
{1, 2, 3, 4, 5, 6}
6. Find the union of sets P = {1, 2, 3, 4, 5} and Q = {4, 5,
6, 7}. Write the result in roster form.
7. Calculate the intersection of sets X = {a, b, c} and Y =
{b, c, d}. Write the result in set-builder notation.
8. Consider two sets: M = {1, 2, 3, 4} and N = {3, 4, 5, 6}.
Find the difference M - N.
9. Solve the following set equation for set Z: Z ∩ {2, 3, 4}
= {3, 4}. Write the result in roster form.
10. Given the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9,
10}, find the complement of the set V = {2, 4, 6, 8}.
**Additional Challenging Questions:**
11. Let A = {1, 2, 3, 4, 5, 6} and B = {4, 5, 6, 7, 8, 9}.
Find A ∪
B, A ∩ B, and A - B.
12. Consider a universal set U = {x | x is a positive
integer less than 10}. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A ∩ B and
A ∪
B.
13. Let U = {a, b, c, d, e, f, g} be the universal set. If A
= {a, b, c, d} and B = {b, c, e, f}, find A ∪ B and A' (complement of A).
14. Define three sets A, B, and C as follows:
A = {x | x is a
multiple of 2 and 3}
B = {x | x is a
multiple of 2 and 5}
C = {x | x is a
multiple of 3 and 5}
Find A ∩ B, A ∪
C, and B ∩ C.
15. Let U be the set of all students in a school, A be the
set of students who play chess, and B be the set of students who play cricket.
If there are 120 students in total, 60 play chess, and 80 play cricket, how
many students play both chess and cricket?
16. Consider the set P = {x | x is a prime number less than
20} and the set Q = {x | x is an odd number less than 20}. Find P ∩ Q.
17. Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}. Find
the symmetric difference of sets A and B.
18. Determine whether the following statement is true or
false: For any two sets A and B, A ∪ B = B ∪ A.
**Answers:**
1. A set is a collection of distinct objects or elements.
Example: Set of even numbers less than 10 = {2, 4, 6, 8}.
2.
a) Set of days of
the week = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
b) Set of even
numbers less than 20 = {2, 4, 6, 8, 10, 12, 14, 16, 18}
c) Set of vowels in
the English alphabet = {a, e, i, o, u}
3. Set A = {2, 4, 6, 8, 10}, Cardinality of A = 5.
4. Set B = {2, 3, 5, 7}. In set-builder notation: B = {x | x
is a prime number and 1 < x < 10}.
5.
a) True
b) False
c) True
6. P ∪ Q = {1, 2, 3, 4, 5, 6, 7}.
7. X ∩ Y = {b, c}. In set-builder notation: {x | x is an
element of X and x is an element of Y}.
8. M - N = {1, 2}. (Elements in M but not in N)
9. Z = {3, 4}.
10. U - V = {1, 3, 5, 7, 9}.
**Answers to Additional Questions:**
11. A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A ∩ B = {4, 5, 6}, A - B = {1, 2, 3}
12. A ∩ B = {3, 4}, A ∪ B = {1, 2, 3, 4, 5, 6}
13. A ∪ B = {a, b, c, d, e, f}, A' = {e,
f, g}
14. A ∩ B = {x | x is a multiple of 2, 3, and 5}, A ∪
C = {x | x is a multiple of 2 or 3 or 5}, B ∩ C
= {x | x is a multiple of 3 and 5}
15. Students who play both chess and cricket = 20 students.
16. P ∩ Q = {3, 5, 7, 11, 13, 17, 19}
17. Symmetric difference of sets A and B = {1, 2, 6, 7}
18. True. The union of two sets is commutative, so A ∪
B = B ∪
A.
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