Sets Class 8 Worksheet 1 with Answers
1.
Fill in the blanks.
a.
If A ⊆ B, then A
– B = ___________.
b.
If n(A ∪ B) = 75,
n(A) = 60, n(B) = 30, then n(B ∩ A ) = ___________.
c. Two sets are overlapping if A ∩ B ≠ ___________.
2. If P =
{letters of the word EXAMINATION} and Q = {letters of the word COMBINATION},
then find
a. P ∩ Q
b. P ∪ Q
c. n (P)
d. n (Q)
e. P – Q
3.
If A = {1, 3, 5, 7, 9, 11} and B = {2, 3, 5, 8, 10, 12}, then match the following:
a.
A ∩ B i. {1, 7, 9, 11}
b.
A – B ii. {1,
2, 3, 5, 7, 8, 9, 10, 11, 12}
c.
B – A iii. {3,
5}
d.
A ∪ B iv. {2, 8, 10, 12}
4.
If A = {a, b, c, d},
B = {d, e, f, h} and C = {c, d, f,
h}, then find
a. A – B
b. B – A
c. (A− B) ∪ (B−A)
d. B – C
e. A – C
f. (B− C) ∩ (A− C)
5. If A = {3, 6, 9, 12, 15, 18, 21}, B =
{2, 4, 6, 8, 10, 12} and C = {6, 12, 18, 24}, then
a. Find
i. n (A ∪ B)
ii. (A ∩ C) ∪ (B ∩ C)
iii. (B ∪ C) ∩ A
iv. n (A ∪ C)
b. Write A, B, C in set builder form.
6.
Given x is the universal set and x = {a,
b, c, d, e, f, g, h}. If A = {a,
b, c, d} and B = {c, d, g, h},
then represent the following using Venn diagram.
a. (A ∪ B)’
b. (A
∩ B)’
Verify
that (A ∪ B)’ = A’ ∩
B’ and (A ∩ B)’ = A’ ∪ B’
7.
State true or false.
a.
In Venn diagram, sets are represented by closed figures like circles, rectangle
or ovals.
b.
Union of set A and its complement is U.
c.
If A and B are two overlapping sets, then A ∩ B = Ï•
d.
If n(A ∪ B) = n(A)
+ n(B), then A ∩ B = Ï•
e.
If n(A ∪ B) = 25, n(A)
= 15 and n(B) = 20, then n (A ∩ B) = 5
f. If A ∩ B = A ∪
B, then A and B are equal sets.
8. If A =
{7 days of the week} and B = {days of the week starting with letter T}, then
find
a. A ∩ B
b. A ∪ B
c. B – A
9.
Let A = {x : x ∈ N and x is an even number
less than or equal to 20} and B = {a, b, c, d}.
a.
List the elements of A
b.
Find n (A)
c.
Find n (A ∪ B)
d. Find A ∩ B
e. Verify that n (A ∩ B) = n (A) + n (B) – n (A ∪ B)
10.
Choose the correct option.
a.
Union of two sets is
i. associative
ii. distributive
iii. commutative
iv. none of these
b.
In case of disjoint sets, A ∩ B is
i. A ii. B
iii. Ï• iv. A ∪ B
c.
If A ⊆ B, then A
∪ B is
i. B ii. A
iii. A ∩ B iv. null set
Sets Class 8 Worksheet 2 with Answers
1.
Choose the correct answer for each of the following:
a.
If A = {12, 13, 14, 15, 16, 17, 18, 19, 21} and B = {x : x is a
multiple of 3}, then A ∩ B
is
i. {14, 21}
ii. {12, 15, 18, 21}
iii. {12, 14, 16, 18}
iv. {13, 17, 19}
b. If A = {prime numbers less than 10}, B =
{even numbers less than 8}, then A ∪ B is
i. {2, 3, 5, 7}
ii. {2, 4, 6}
iii. {2, 3, 4, 5, 6, 7}
iv. {2}
c. A and B are two disjoint sets. If n (A) =
10, n (B) = 8, then n (A ∪ B) is
i. 10 ii. 2
iii. 18 iv. 0
d. If A = {letters of the word KOLKATA} and B
= {letters of the word KARNATAKA}, then A and B are two
i. disjoint sets
ii. overlapping sets
iii. equivalent sets
iv. equal sets
e. If A = {vowels in the word
THIRUVANATHAPURAM}, then A is
i. {T, H, R, V, N, T, H, P, R, M}
ii. {A, R, H, T, M}
iii. {A, I, U}
iv.
{T, H, I, R, U, V, A, N}
2. Let A = {1, 2, 3, 4, 5, 6, 7}, B = {2,
4, 6, 8} and C = {2, 3, 5, 7}, then find the following:
a. A ∩ B
b. A ∪ B
c. (B ∩ C) ∪ A
d. n (A)
e. n(A ∩ C)
f. (A ∪ C) ∩ B
3.
State true or false.
a.
If A ⊆ B, then A
∩ B = B
b.
If A − B = Ï•, then A is a subset of B.
c.
If A′ represents the complement of set A, then A ∩ A′ = ξ is the universal set.
4. Draw a Venn diagram to illustrate A ⊆ B, where A = {1, 2, 3, 4} and B is
the set of first two natural numbers.
5.
If the set of natural numbers is the universal
set, A is the set of first 20 even natural numbers and B is the set of first 10
multiples of 3. Represent this using Venn diagram and hence find A ∩ B.
6.
Let A = {x: x ∈ N, x is a multiple of
3, x ≤ 18} and B = {x: x ∈ W, x is a multiple of
2, x ≤ 18}.
a.
List the elements of A and B.
b. Find:
i. n (A ∩ B)
ii. n (A ∪ B)
7.
In a group of 30 students, 10 like football
but not cricket, 12 like cricket but not football and 5 like both cricket and
football. Find the following using Venn diagram.
a.
How many like football?
b.
How many like cricket?
c.
How many like none of the games?
8. Let A = {letters of the word
MANCHESTER} and B = {letters of the word YORKSHIRE}.
a. List the elements of:
i. A ii. B
b. Find:
i. n (A) ii. A ∩ B
iii. n (A ∪ B)
c. Verify that n (A ∩ B) = n (A) + n (B) – n (A ∪ B).
9.
Given A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20,
22, 24}, B = {–5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6} and C = {1, 4, 9, 16,
25, 36}. Represent the following using Venn diagram.
a. A – B
b. B – C
c. A – C
10.
Draw the Venn diagram to show the following
relationship between the sets.
a. A ⊂ B
b. A ∩ B = A
c. A ∪ B = C
11.
Fill in the blanks.
a.
If A = {the letters of the word ROSES}, then n (A) is ___________.
b.
If B = {2, 4, 6, 8, 10}, then B in set builder form is ___________.
c.
If P = {5, 10, 15, 20, 25, 30} and Q = {2, 5, 8, 10, 14, 15}, then P ∪ Q
is ___________.
d. A = {colour of the rainbow} and B = {green,
yellow, red}, then n (A ∩ B) = ___________.
e. If A = {letters of the word BIRTHDAY} and B
= {letters of the word THIRD}, then n (A ∪ B)
is equal to ___________.
Worksheet 1
1. a. Ï• b. 15
c. Ï•
2. a. P ∩ Q = {A, M, I, N,
T, O}
b. P ∪ Q = {E, X, A, M,
I, N, T, O, C, B, T}
c. n (P) = 8
d. n (Q) = 8
e. P – Q
= {E, X}
3. a. iii b. i
c. iv d. ii
4. a. A – B = {a,
b, c}
b. B – A = {e, f, h}
c. (A − B) ∪
(B − A) = {a, b, c, e, f, h}
d. B – C = {e}
e. A – C = {a, b}
f. (B − C) ∩ (A − C) = {a, b,
e}
5. a. i. n (A ∪ B) = 11
ii.
(A ∩ C) ∪ (B ∩ C) = {6, 12, 18}
iii. (B ∪ C) ∩ A = {6, 12, 18}
iv. n (A ∪ C) = 8
b. A = {x: x = 3n; n ∈ N; n < 8}
B = {x: x = 2n; n ∈ N; n < 7}
C = {x: x = 6n; n ∈ N; n < 5}
6. a. (A ∪ B)’ = {e, f}
b. (A ∩ B)’ = {a, b, e, f, g, h}
7. a. True b. True
c. False d. True
e. False e. True
8. a. A ∩ B = {Tuesday, Thursday}
b. A
∪ B = {7 days of the week}
c. B
– A = Ï•
9. a. A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
b.
n(A) = 10
c. n(A
∪ B) = 14
d. A
∩ B = Ï•
10. a. iii b. iii
c.
i
Worksheet
2
1. a. ii b. iii
c.
iii d. ii
e. iii
2. a. A ∩ B = {2, 4, 6}
b. A
∪ B = {1, 2, 3, 4, 5, 6, 7, 8}
c.
(B ∩ C) ∪ A = {1, 2, 3, 4, 5, 6, 7}
d. n(A) = 7
e. n(A ∩ C) = 4
f. (A ∪ C) ∩ B = {2, 4, 6}
3. a. False b. True
c. False
4. Do it yourself
5. A ∩ B = {6, 12,
18, 24, 30}
6. a. A = {3, 6, 9, 12, 15, 18}
B = {2, 4, 6, 8, 10, 12, 14, 16, 18}
b. i.
n (A ∩ B) = 3
ii.
n (A ∪ B) = 12
7. a. 15 b. 17
c. 2
8. a. i. A = {M, A, N, C, H, E, S, T, R}
ii. B = {Y, O, R, K, S, H, I, E}
b.
i. n(A) = 9
ii. n(B) = 8
iii. n (A ∪ B) = 13
9. Do it yourself
10. Do it yourself
11. a. 4
b.
{x: x = 2n; n ∈
N; n < 6}
c.
{2, 5, 8, 10, 14, 15, 20, 25, 30}
d. 3
e. 8
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| Maths Worksheets for Other Chapters of Class 8 |
1. Rational numbers class 8 worksheet
2. Exponents and powers class 8 worksheet
3. Squares and square roots class 8 worksheets
4. Cubes and cube roots class 8 worksheets
5. Playing with numbers class 8 worksheet
6. Algebraic expressions class 8 worksheet
7. Factorisation class 8 worksheet
8. Linear equations in one variable class 8 worksheet
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10. Compound interest class 8 worksheets
11. Direct and inverse proportions class 8 worksheets
12. Understanding quadrilaterals class 8 worksheets
13. Construction of quadrilaterals class 8 worksheet
14. Perimeter and area class 8 worksheets
15. Surface area and volume class 8 worksheets
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17. Probability class 8 worksheets
Some Extra Worksheets for ICSE Maths Class 8
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