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9th maths 1st unit assignment – Question Only download here
Assignment
Class:9 Subject:Mathematics
Unit 1- Set Theory
Part- A
I. 1 Mark Questions :
1.Consider the set A={10, 15, 20, 25}. Fill in the blanks with the appropriate symbol ∈ or €
i) 10………. A ii) 23…….. A
Answer:- i) 10 ∈ A ii) 23 € A
2.Write set of letters of the following word in Roster Form
“MATHEMATICS”
Answer:- A={M,A,T,H,E,I,C,S}
3.If A={8, 10, 12, 14, 16, 18, 20} find n(A)
a. 4 b. 8 c. 7 d. 6
Answer:- c. 7
4.If A={4, 5, 6}and B={3, 5, 7} (A∩B)
a. { 5 } b. { 4 } c. { 5, 6 } d. { 5, 7 }
Answer:- a. { 5 }
5.Which of the following is correct?
a. ∅⊂ { a, b } b. ∅∈ { a, b } c. {a} ∈ { a, b } d. a ∈ { a, b }
Answer:- a. ∅⊂ { a, b }
6.Which of the following is correct?
a. { 8 } ∈ { 1, 2, 3, 7 } b. { 8 } € { 1, 2, 3, 7 }
c. 7 ∈{ 1, 2, 3, 7 } d. { 7 } € { 1, 2, 3}
Answer:- a. { 8 } ∈ { 1, 2, 3, 7 }
7.Which of the following is true?
a. A-B=(A∩B) b. A-B=B-A
c. (A∪B)’ = A’∪B’ d. (A∩B)’ = A∪B’
Answer:- d. (A∩B)´ = A´∪B´
8.If A and B are disjoint sets then n(A ∪ B) = n(A) + n(B). This statement is
a. True b. False
Answer:- b. False
9.Fill in the blank
A- (B ∩ C) = _____
Answer:- (A-B)∪(A-C)
10.For any two sets A and B
i). A ∪ B = B ∪ A ii). A ∩ B= B ∩ A this property is
a). Associate Property b). Distributive Property
c). Commutative Property d). None of these.
Answer:- a). Associate Property
Part- B
II. Short Answer:
1.If A={2,5,7,8,9} and B= {7,8,10,11} find A Δ B
Answer
A -B = {2,5,9 }
B-A = {10,11}
AΔB = (A-B) ∪ (B_A)
= { 2,5,9 } ∪ {10,11}
= {2,5,9,10,11}
2.Find the Number of subsets & the number of proper subsets of a set A ={x,y,z,p,q}.
Anwer
Given A = {x,y,z,p,q}
n(A) = 5
No.of Subsets =2m = 25 = 2x2x2x2x2x = 32
No.of Proper Subsets = 2m-1 = 25 -1 = 32-1 = 31
3.Write the set of letters of the following words in Roster form,
i). ASSIGNMENT ii). TEACHER
Answer
i) {A,S,I,G,N,M,E,T}
ii){T,E,A,C,H,R}
4.A={1,2,5,7,9}, Q={2,3,5,9,11}, R={3,4,5,7,9} and S={2,3,4,5,8}, then find
i). (P ∪ Q) ∪ R ii). (Q ∩ S) ∩ R
Answers
i) (P ∪ Q) = {1,2,5,7,9} ∪ {2,3,5,9,11}
= {1,2,3,5,7,9,11}
(P ∪ Q) ∪ R = {1,2,3,5,7,9,11} ∪ {3,4,5,7,9}
= {1,2,3,4,5,7,9,11}
ii) (Q ∩ S) ={2,3,5,9,11} ∩ {2,3,4,5,8}
= {2,3,5}
(Q ∩ S) ∩ R = {2,3,5} ∩ {3,4,5,7,9}
= {3,5}
5.If n(A) = 20, n(B) = 50, n(A U B) = 60 and n(B’ ) = 20, find n(A ∩ B) and n(U)
n(A U B) = n(A) + n (A ∩ B)
60 = 20 + 50 – n (A ∩ B)
60 = 70 – n (A ∩ B)
b(A ∩ B) = 70-60
n(A ∩ B) = 10
n( U ) = n(B) + n (B’)
= 50+20
=70
Part- C
III. Answer the following:
1.Let X={a, e, i, o, u}and Y={a, g, o, f}. Verify that n(A-B) = n(A) – n(A∩B)
2.Out of 500 Car owners investigated, 400 owned Car A and 200 Owned Car B, 50 Owned
both A and B Cars. Is this data Correct?
Solution:
n( A ∪ B) = n(A) + n(B) – n( A ∩ B)
n(A ∪ B) = 500 (given) …………. (1).
n( A) = 400
n(B) = 200
n( A ∩ B) =50
∴ n(A ∩ B) = 400 + 200 – 50 = 550 …………… (2)
1 ≠ 2
∴ This data is incorrect.
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