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

1.	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» 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.

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»

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.