{"id":580966,"date":"2022-02-22T10:26:45","date_gmt":"2022-02-22T10:26:45","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=580966"},"modified":"2022-02-25T04:43:39","modified_gmt":"2022-02-25T04:43:39","slug":"maharashtra-board-solutions-class-9-maths-part-1-chapter-1-3-sets","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/maharashtra-board-solutions-class-9-maths-part-1-chapter-1-3-sets\/","title":{"rendered":"Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 1.3- Sets"},"content":{"rendered":"\n

Class 9: Maths Chapter 1.3 solutions. Complete Class 9 Maths Chapter 1.3 Notes.<\/p>\n\n\n\n

Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 1.3- Sets<\/h2>\n\n\n\n

Maharashtra Board 9th Maths Chapter 1.3, Class 9 Maths Chapter 1.3 solutions<\/p>\n\n\n\n

Question 1.
If A = {a, b, c, d, e}, B = {c, d, e, f}, C = {b, d}, D = {a, e}, then which of the following statements are true and which are false?<\/strong>
i. C \u2286 3
ii. A \u2286 D
iii. D \u2286 B
iv. D \u2286 A
V. B \u2286 A
vi. C \u2286 A
Ans:
<\/strong>i. C = {b, d}, B = {c, d, e ,f}
C \u2286 B
False
Since, all the elements of C are not present in B.<\/p>\n\n\n\n

ii. A = {a, b, c, d, e}, D = {a, e}
A \u2286 D
False
Since, all the elements of A are not present in D.<\/p>\n\n\n\n

iii. D = {a, e}, B = {c, d, e, f}
D \u2286 B
False
Since, all the elements of D are not present in B.<\/p>\n\n\n\n

iv. D = {a, e}, A = {a, b, c, d, e}
D \u2286 A
True
Since, all the elements of D are present in A.<\/p>\n\n\n\n

v. B = {c, d, e, f}, A = {a, b, c, d, e}
B \u2286 A
False
Since, all the elements of B are not present in A.<\/p>\n\n\n\n

vi. C = {b, d}, A= {a, b, c, d, e}
C \u2286A
True
Since, all the elements of C are present in A.<\/p>\n\n\n\n

Question 2.
Take the set of natural numbers from 1 to 20 as universal set and show set X and Y using Venn diagram. [2 Marks each]<\/strong>
i. X= {x |x \u2208 N, and 7 < x < 15}
ii. Y = { y | y \u2208 N, y is a prime number from 1 to 20}
Answer:
<\/strong>i. U = {1, 2, 3, 4, \u2026\u2026.., 18, 19, 20}
x = {x | x \u2208 N, and 7 < x < 15}
\u2234 x = {8, 9, 10, 11, 12, 13, 14}
\"Maharashtra<\/p>\n\n\n\n

ii. U = {1, 2, 3, 4, \u2026\u2026 ,18, 19, 20}
Y = { y | y \u2208 N, y is a prime number from 1 to 20}
\u2234 Y = {2, 3, 5, 7, 11, 13, 17, 19}
\"Maharashtra<\/p>\n\n\n\n

Question 3.
U = {1, 2, 3, 7, 8, 9, 10, 11, 12} P = {1, 3, 7,10}, then
<\/strong>i. show the sets U, P and P\u2019 by Venn diagram.
ii. Verify (P\u2019)\u2019 = P
Solution:
<\/strong>i. Here, U = {1,2, 3, 7, 8,9, 10, 11, 12} P = {1, 3, 7, 10}
\u2234 P\u2019 = {2, 8, 9, 11, 12}
\"Maharashtra<\/p>\n\n\n\n

II. Here, U = {1, 2, 3, 7, 8, 9, 10, 11, 12}
P = {1, 3, 7, 10} \u2026.(i)
\u2234 P\u2019= {2, 8, 9, 11, 12}
Also, (P\u2019)\u2019 = {1,3,7, 10} \u2026(ii)
\u2234 (P\u2019)\u2019 = P \u2026 [From (i) and (ii)]<\/p>\n\n\n\n

Question 4.
A = {1, 3, 2, 7}, then write any three subsets of A.
Solution:<\/strong>
Three subsets of A:
i. B = {3}
ii. C = {2, 1}
iii. D= {1, 2, 7}
[Note: The above problem has many solutions. Students may write solutions other than the ones given]<\/p>\n\n\n\n

Question 5.<\/strong>
i. Write the subset relation between the sets.
P is the set of all residents in Pune.
M is the set of all residents in Madhya Pradesh.
I is the set of all residents in Indore.
B is the set of all residents in India.
H is the set of all residents in Maharashtra.<\/p>\n\n\n\n

ii. Which set can be the universal set for above sets ?
Solution:<\/strong>
i.
a. The residents of Pune are residents of India.
\u2234 P \u2286 B
b. The residents of Pune are residents of Maharashtra.
\u2234 P \u2286 H
c. The residents of Madhya Pradesh are residents of India.
\u2234 M \u2286 B
d. The residents of Indore are residents of India.
\u2234 I \u2286 B
e. The residents of Indore are residents of Madhya Pradesh.
\u2234 I \u2286 M
f. The residents of Maharashtra are residents of India.
\u2234 H \u2286B<\/p>\n\n\n\n

ii. The residents of Pune, Madhya Pradesh, Indore and Maharashtra are all residents of India.
\u2234 B can be the Universal set for the above sets.<\/p>\n\n\n\n

Question 6.
Which set of numbers could be the universal set for the sets given below?<\/strong>
i. A = set of multiples of 5,
B = set of multiples of 7,
C = set of multiples of 12<\/p>\n\n\n\n

ii. P = set of integers which are multiples of 4.
T = set of all even square numbers.
Answer:
<\/strong>i. A = set of multiples of 5
\u2234 A = {5, 10, 15, \u2026}
B = set of multiples of 7
\u2234 B = {7, 14, 21,\u2026}
C = set of multiples of 12
\u2234 C = {12, 24, 36, \u2026}
Now, set of natural numbers, whole numbers, integers, rational numbers are as follows:
N = {1, 2, 3, \u2026}, W = {0, 1, 2, 3, \u2026}
I = {\u2026,-3, -2, -1, 0, 1, 2, 3, \u2026}
Q = { pq | p,q \u2208 I,q \u2260 0}
Since, set A, B and C are the subsets of sets N, W , I and Q.
\u2234 For set A, B and C we can take any one of the set from N, W, I or Q as universal set.<\/p>\n\n\n\n

ii. P = set of integers which are multiples of 4.
<\/strong>P = {4, 8, 12,\u2026}
T = set of all even square numbers T = {22<\/sup>, 42<\/sup>, 62<\/sup>, \u2026]
Since, set P and T are the subsets of sets N, W, I and Q.
\u2234 For set P and T we can take any one of the set from N, W, I or Q as universal set.<\/p>\n\n\n\n

Question 7.
Let all the students of a class form a Universal set. Let set A be the students who secure 50% or more marks in Maths. Then write the complement of set A.
Answer:<\/strong>
Here, U = all the students of a class.
A = Students who secured 50% or more marks in Maths.
\u2234 A\u2019= Students who secured less than 50% marks in Maths.<\/p>\n\n\n\n

Question 1.
If A = {1, 3, 4, 7, 8}, then write all possible subsets of A.
i. e. P = {1, 3}, T = {4, 7, 8}, V = {1, 4, 8}, S = {1, 4, 7, 8}
In this way many subsets can be written. Write five more subsets of set A. (Textbook pg. no, 8)
Answer:<\/strong>
B = { },
E = {4},
C = {1, 4},
D = {3, 4, 7},
F = {3, 4, 7,8}<\/p>\n\n\n\n

Question 2.
Some sets are given below.<\/strong>
A ={\u2026,-4, -2, 0, 2, 4, 6,\u2026}
B = {1, 2, 3,\u2026}
C = {\u2026,-12, -6, 0, 6, 12, 18, }
D = {\u2026, -8, -4, 0, 4, 8,\u2026}
I = {\u2026,-3, -2, -1, 0, 1, 2, 3, 4, }
Discuss and decide which of the following statements are true.
a. A is a subset of sets B, C and D.
b. B is a subset of all the sets which are given above. (Textbook pg. no. 9)
Solution:
<\/strong>a. All elements of set A are not present in set B, C and D.
\u2234 A \u2286 B,
\u2234 A \u2286 C,
\u2234 A \u2286 D
\u2234 Statement (a) is false.<\/p>\n\n\n\n

b. All elements of set B are not present in set A, C and D.
\u2234 B \u2286 A,
\u2234 B \u2286 C,
\u2234 B \u2286 D
\u2234 Statement (b) is false.<\/p>\n\n\n\n

Question 3.
Suppose U = {1, 3, 9, 11, 13, 18, 19}, and B = {3, 9, 11, 13}. Find (B\u2019)\u2019 and draw the inference. (Textbook pg. no. 10)
\"Maharashtra
Solution:<\/strong>
U = {1, 3, 9, 11, 13, 18, 19},
B= {3, 9, 11, 13} \u2026.(i)
\u2234 B\u2019= {1, 18, 19}
(B\u2019)\u2019= {3, 9, 11, 13} \u2026.(ii)
\u2234 (B\u2019)\u2019 = B \u2026 [From (i) and (ii)]
\u2234 Complement of a complement is the given set itself.<\/p>\n\n\n\n

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Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 1.3- Sets<\/p>\n\n\n\n

Download PDF<\/strong>: Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 1.3- Sets PDF<\/a><\/p>\n\n\n\n

Chapterwise Maharashtra Board Solutions Class 9 Maths :<\/strong><\/h2>\n\n\n\n

Part 1<\/strong><\/p>\n\n\n\n