Question

4) Write with reasons, which of the following sets are finite or infinite.
(i) A = {x|x < 10, x is a natural number} (v) Set of apparatus in laboratory
(ii) B = {yly< -1. y is an integer}
(vi) Set of whole numbers
(iii) C = Set of students of class 9 from your school. (vii) Set of rational number
(iv) Set of people from your village.​

Answer 1

Given :  (i) A = {x|x < 10, x is a natural number} , (ii) B = {yly< -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  

To find : sets are finite or infinite.

Solution:

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

{ 1 , 2 , 3 , 4 ,5 , 6 , 7 , 8 , 9 }

Finite

(ii) B = {yly< -1. y is an integer}

=> B = { -∞ ,.............., -1, 0)

Infinite

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

There will be countable number of students in class 9 in your school

Hence  Finite

(iv) Set of people from your village.

There will be countable  number of people in village

Hence Finite

v)  Set of apparatus in laboratory

apparatus in laboratory can be counted  ( in a specified laboratory)

We can identify each & every apparatus  and label them

and can maintain the records.

Hence Finite

(vi) Set of whole numbers

can not be counted

infinite

(vii) Set of rational number  

can not be counted

infinite

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