Maharashtra State Board
Chapter 1: Sets
Practice Set 1.3 Solutions
Q.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?
 |
| We consider the following Venn diagram to check whether the above
statements are true or not. Now, we have A = {a, b, c, d, e}, B = {c, d, e, f}, C = {b, d} and D = {a, e}. |
(i) C ⊆ B
Answer: True (Because {b, d} ⊆ {c, d, e, f} is not correct → Actually False)
Correct: False
(ii) A ⊆ D
Answer: False (Because A = {a,b,c,d,e}, D = {a,e}, A is not contained in D)
(iii) D ⊆ B
Answer: False (Because D = {a,e}, but 'a' ∉ B)
(iv) D ⊆ A
Answer: True (Because {a,e} ⊆ {a,b,c,d,e})
(v) B ⊆ A
Answer: False (Because f ∈ B but f ∉ A)
(vi) C ⊆ A
Answer: True (Because {b,d} ⊆ {a,b,c,d,e})
Q.2 Take the set of natural numbers from 1 to 20 as universal set and show set X and Y.
(i) X = { x | x ∈ N, 7 < x < 15 }
Answer: X = {8, 9, 10, 11, 12, 13, 14}
(ii) Y = { y | y ∈ N, y is prime number from 1 to 20 }
Answer: Y = {2, 3, 5, 7, 11, 13, 17, 19}
Q.3 U = {1, 2, 3, 7, 8, 9, 10, 11, 12}, P = {1, 3, 7, 10} (i) Show the sets U, P and P′ by Venn diagram. (ii) Verify (P′)′ = P.
Answer (i): U = {1,2,3,7,8,9,10,11,12}
P = {1,3,7,10}
P′ = {2,8,9,11,12}
Answer (ii): (P′)′ = {1,3,7,10} = P ✔
Q.4 A = {1, 3, 2, 7}, then write any three subsets of A.
Answer: Examples of subsets:
{1,3}, {2,7}, {1,2,3}
Q.5 (i) Write the subset relation between the sets.
P = Residents in Pune
M = Residents in Madhya Pradesh
I = Residents in Indore
B = Residents in India
H = Residents in Maharashtra
Answer:
P ⊆ H, I ⊆ M, H ⊆ B, M ⊆ B
(ii) Which set can be the universal set for above?
Answer: B (set of all residents in India)
Q.6 Which set of numbers could be the universal set for the sets given below?
(i) A = multiples of 5, B = multiples of 7, C = multiples of 12
Answer: Universal set = Set of all natural numbers (or set of all integers)
(ii) P = integers which are multiples of 4, T = all even square numbers
Answer: Universal set = Set of all integers
Q.7 Let all the students of a class is an Universal set. Let set A = students securing 50% or more marks in Maths. Write the complement of set A.
Answer: A′ = {students who secure less than 50% marks in Maths}
Class 9 Maths Digest
- Practice Set 1.1 Class 9 Answers
- Practice Set 1.2 Class 9 Answers
- Practice Set 1.3 Class 9 Answers
- Practice Set 1.4 Class 9 Answers
- Problem Set 1 Class 9 Answers
- Practice Set 2.1 Class 9 Answers
- Practice Set 2.2 Class 9 Answers
- Practice Set 2.3 Class 9 Answers
- Practice Set 2.4 Class 9 Answers
- Practice Set 2.5 Class 9 Answers
- Problem Set 2 Class 9 Answers
