## Maharashtra State Board Class 9 Maths Solutions Chapter 1 Sets 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 e N, x < 2}

Solution:

A= {x | 3x – 1 = 2}

Here, 3x – 1 = 2

∴ 3x = 3

∴ x = 1

∴ A = {1} …(i)

B = {x | x is a natural number but x is neither prime nor composite}

1 is the only number which is neither prime nor composite,

∴ x = 1

∴ B = {1} …(ii)

C = {x | x G N, x < 2}

1 is the only natural number less than 2.

∴ x = 1

∴ C = {1} …(iii)

∴ The element in sets A, B and C is identical. … [From (i), (ii) and (iii)]

∴ A, B and C are 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}

Solution:

A = Even prime numbers

Since 2 is the only even prime number,

∴ A = {2} …(i)

B= {x | 7x – 1 = 13}

Here, 7x – 1 = 13

∴ 7x = 14

∴ x = 2

∴ B = {2} …(ii)

∴ The element in set A and B is identical. … [From (i) and (ii)]

∴ A and 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 | x^{2} = 0}

iii. C = {x | 5x – 2 = 0, x ∈N}

Solution:

i. A = {a| a is a natural number smaller than zero}

Natural numbers begin from 1.

∴ A = { }

∴ A is an empty set.

ii. B = {x | x^{2} = 0}

Here, x^{2} = 0

∴ x = 0 … [Taking square root on both sides]

∴ B = {0}

∴B is not an empty set.

iii. C = {x | 5x – 2 = 0, x ∈ N}

Here, 5x – 2 = 0

∴ 5x = 2

∴ x = \(\frac { 2 }{ 5 }\)

Given, x ∈ N

But, x = \(\frac { 2 }{ 5 }\) is not a natural number.

∴ C = { }

∴ C is an empty set.

Question 4.

Write with reasons, which of the following sets are finite or infinite.

i. A = {x | x<10, xisa natural number}

ii. B = {y | y < -1, y 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

Solution:

i. A={x| x < 10, x is a natural number}

∴ A = {1,2, 3,4, 5,6, 7, 8, 9}

The number of elements in A are limited and can be counted.

∴A is a finite set.

ii. B = (y | y < -1, y is an integer}

∴ B = { …,-4, -3, -2}

The number of elements in B are unlimited and uncountable.

∴ B is an infinite set.

iii. C = Set of students of class 9 from your school.

The number of students in a class is limited and can be counted.

∴ C is a finite set.

iv. Set of people from your village.

The number of people in a village is limited and can be counted.

∴ Given set is a finite set.

v. Set of apparatus in laboratory

The number of apparatus in the laboratory are limited and can be counted.

∴ Given set is a finite set.

vi. Set of whole numbers

The number of elements in the set of whole numbers are unlimited and uncountable.

∴ Given set is an infinite set.

vii. Set of rational number

The number of elements in the set of rational numbers are unlimited and uncountable.

∴ Given set is an infinite set.

Question 1.

If A = {1, 2, 3} and B = {1, 2, 3, 4}, then A ≠ B verify it. (Textbook pg. no. 6)

Answer:

Here, 4 ∈ B but 4 ∉ A

∴ A and B are not equal sets,

i.e. A ≠ B

Question 2.

A = {x | x is prime number and 10 < x < 20} and B = {11,13,17,19}. Here A = B. Verify. (Textbook pg. no. 6)

Answer:

A = {x | x is prime number and 10 < x < 20}

∴ A = {11, 13, 17, 19}

B = {11, 13, 17, 19}

∴ All the elements in set A and B are identical.

∴ A and B are equal sets, i.e. A = B