Practice Set 1.3 Algebra 9th Std Maths Part 1 Answers Chapter 1 Sets
ii. A = {a, b, c, d, e}, D = {a, e}
A ⊆ D
False
Since, all the elements of A are not present in D.
iii. D = {a, e}, B = {c, d, e, f}
D ⊆ B
False
Since, all the elements of D are not present in B.
iv. D = {a, e}, A = {a, b, c, d, e}
D ⊆ A
True
Since, all the elements of D are present in A.
v. B = {c, d, e, f}, A = {a, b, c, d, e}
B ⊆ A
False
Since, all the elements of B are not present in A.
vi. C = {b, d}, A= {a, b, c, d, e}
C ⊆A
True
Since, all the elements of C are present in A.
Question 2
Maharashtra Board Solution
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] i. X= {x |x ∈ N, and 7 < x < 15} ii. Y = { y | y ∈ N, y is a prime number from 1 to 20}
Solution & Step-by-Step Answer:
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Solution & Step-by-Step Answer:
i. U = {1, 2, 3, 4, …….., 18, 19, 20} x = {x | x ∈ N, and 7 < x < 15} ∴ x = {8, 9, 10, 11, 12, 13, 14}
ii. U = {1, 2, 3, 4, ……,18, 19, 20}
Question 3
Maharashtra Board Solution
U = {1, 2, 3, 7, 8, 9, 10, 11, 12} P = {1, 3, 7,10}, then i. show the sets U, P and P’ by Venn diagram. ii. Verify (P’)’ = P
Solution & Step-by-Step Answer:
i. Here, U = {1,2, 3, 7, 8,9, 10, 11, 12} P = {1, 3, 7, 10} ∴ P’ = {2, 8, 9, 11, 12}
II. Here, U = {1, 2, 3, 7, 8, 9, 10, 11, 12}
Question 4
Maharashtra Board Solution
A = {1, 3, 2, 7}, then write any three subsets of A.
Solution & Step-by-Step Answer:
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]
Question 5
Maharashtra Board Solution
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. |
ii. Which set can be the universal set for above sets ?
i.
a. The residents of Pune are residents of India.
∴ P ⊆ B
b. The residents of Pune are residents of Maharashtra.
∴ P ⊆ H
c. The residents of Madhya Pradesh are residents of India.
∴ M ⊆ B
d. The residents of Indore are residents of India.
∴ I ⊆ B
e. The residents of Indore are residents of Madhya Pradesh.
∴ I ⊆ M
f. The residents of Maharashtra are residents of India.
∴ H ⊆B
ii. The residents of Pune, Madhya Pradesh, Indore and Maharashtra are all residents of India.
∴ B can be the Universal set for the above sets.
Question 6
Maharashtra Board Solution
Which set of numbers could be the universal set for the sets given below? i. A = set of multiples of 5, B = set of multiples of 7, C = set of multiples of 12
ii. P = set of integers which are multiples of 4.
Solution & Step-by-Step Answer:
i. A = set of multiples of 5
∴ A = {5, 10, 15, …} B = set of multiples of 7 ∴ B = {7, 14, 21,…} C = set of multiples of 12 ∴ C = {12, 24, 36, …} Now, set of natural numbers, whole numbers, integers, rational numbers are as follows: N = {1, 2, 3, …}, W = {0, 1, 2, 3, …} I = {…,-3, -2, -1, 0, 1, 2, 3, …} Q = { | p,q ∈ I,q ≠ 0} Since, set A, B and C are the subsets of sets N, W, I and Q. ∴ For set A, B and C we can take any one of the set from N, W, I or Q as universal set. ii. P = set of integers which are multiples of 4.
Question 7
Maharashtra Board Solution
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.
Solution & Step-by-Step Answer:
Here, U = all the students of a class. A = Students who secured 50% or more marks in Maths. ∴ A’= Students who secured less than 50% marks in Maths.
Question 1
Maharashtra Board Solution
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)
Solution & Step-by-Step Answer:
B = { }, E = {4}, C = {1, 4}, D = {3, 4, 7}, F = {3, 4, 7,8}
Question 2
Maharashtra Board Solution
Some sets are given below. A ={…,-4, -2, 0, 2, 4, 6,…} B = {1, 2, 3,…} C = {…,-12, -6, 0, 6, 12, 18, } D = {…, -8, -4, 0, 4, 8,…} I = {…,-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 & Step-by-Step Answer:
a. All elements of set A are not present in set B, C and D. ∴ A ⊆ B, ∴ A ⊆ C, ∴ A ⊆ D ∴ Statement (a) is false.
b. All elements of set B are not present in set A, C and D.
Question 3
Maharashtra Board Solution
Suppose U = {1, 3, 9, 11, 13, 18, 19}, and B = {3, 9, 11, 13}. Find (B’)’ and draw the inference. (Textbook pg. no. 10)
Solution & Step-by-Step Answer:
U = {1, 3, 9, 11, 13, 18, 19}, B= {3, 9, 11, 13} ….(i) ∴ B’= {1, 18, 19} (B’)’= {3, 9, 11, 13} ….(ii) ∴ (B’)’ = B … [From (i) and (ii)] ∴ Complement of a complement is the given set itself.
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