__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.