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.