Practice Set 1.2 Sets Class 9th Mathematics Part I MHB Solution
Practice Set 1.2
Question 1.
Decide which of the following are equal sets and which are not? Justify your answer.
A = {x|3x – 1 = 2}
B = {x | x is a natural number but x is neither prime nor composite}
C = {x |x ∈ N, x < 2}
Answer:
We know that two sets A and B are said to be equal, if every element of set A is in set B and every element of set B is in set A. It is symbolically written as A = B.
A = {x|3x – 1 = 2}
⇒ 3x – 1 = 2
⇒ 3x = 2 + 1 = 3
⇒ x = 3/3 = 1
∴ A = {1}
B = {x |x is a natural number but x is neither prime nor composite}
We know that 1 is neither prime nor composite and is a natural number.
∴ B = {1}
C = {x |x ∈ N, x < 2}
We know that natural number, N = {0, 1, 2, 3, …}
∴ C = {0, 1}
A = B, B ≠ C, A ≠ C
Ans. A and B are equal sets but B and C (and) A and C are not equal sets.
Question 2.
Decide whether set A and B are equal sets. Give reason for your answer.
A = Even prime numbers
B = {x| 7x – 1 = 13}
Answer:
We know that two sets A and B are said to be equal, if every element of set A is in set B and every element of set B is in set A. It is symbolically written as A = B.
A = Even Prime Numbers = {2}
B = {x| 7x – 1 = 13}
⇒ 7x – 1 = 13
⇒ 7x = 13 + 1 = 14
⇒ x = 14/7
∴ x = 2
∴ A = B
Ans. Set A and set B are equal sets.
Question 3.
Which of the following are empty sets? Why?
i. A = {a |a is a natural number smaller than zero.}
ii. B = {x|x2 = 0}
iii. C = {x|5x – 2 = 0, x ∈ N}
Answer:
i. We know that If there is not a single element in the set which satisfies the given condition then it is called a Null set or an Empty set. Empty set is represented by { }.
We know that Natural number, N = {0, 1, 2, … }.
∴ A = {a |a is a natural number smaller than zero} = {}
Ans. A is an empty set.
ii. B = {x|x2 = 0}
⇒ x2 = 0
∴ x = 0
B = {x|x2 = 0} = {0} ≠ {}
Ans. B is not an empty set.
iii. C = {x|5x – 2 = 0, x ∈ N}
⇒ 5x – 2 = 0
⇒ 5x = 2
⇒ x = 5/2
We know that natural number, N = {0, 1, 2,… }
∴ x N
∴ C = {x|5x – 2 = 0, x ∈ N} = {}
Ans. C is an empty set.
Question 4.
Write with reasons, which of the following sets are finite or infinite. We know that if a set is a null set or number of elements are limited and countable then it is called ‘Finite set’ and if number of elements in a set is unlimited and uncountable then the set is called ‘Infinite set’.
i. A = {x|x < 10, x is a natural number}
ii. B = {y |y< -1, is an integer}
iii. C = Set of students of class 9 from your school.
iv. Set of people from your village.
v. Set of apparatus in laboratory
vi. Set of whole numbers
vii. Set of rational number
Answer:
i. A = {x|x < 10, x is a natural number}
∴ A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
Ans. A is a finite set.
ii. B = {y |y< -1, y is an integer}
∴ B = {… -5, -4, -3, -2}
Ans. B is an infinite set.
iii. C = {a, b, c, d, e, …}
Ans. C is an infinite set.
iv. D = {Sarpanch, villager1, villager2, …}
Ans. D is an infinite set.
v. E = {Beakers, funnels, chemicals, thermometers, …}
Ans. E is an infinite set.
vi. W = {1, 2, 3, 4, 5, …}
Ans. W is an infinite set.
vii. Q = {(p/q) |p, q ∈ I, q ≠ 0}
Q = {1/2, 1/3, 1/4, …}
Ans. Q is an infinite set.
