Question

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

Answer 1

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.