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.
Answers
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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