Question

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

( i ) A = { x | x < 10, x is a 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} = {1, 2, 3, 4, 5, 6, 7, 8, 9}

So, A is a finite set.

(ii) B = {y | y < $-$1, y is an integer} = {..., $-$5, $-$4, $-$3, $-$2}

So, B is an infinite set.

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

Since, the number of elements of set C is countable number.

So, C is a finite set.

(iv) D = Set of people from your village.

Since, the number of elements of set D is countable number.

So, D is a finite set.

(v) E = Set of apparatus in laboratory

Since, the number of elements of set E is countable number.

So, E is a finite set.

(vi) F = Set of whole numbers = {0,1, 2, 3, 4, ...}

So, F is an infinite set.

(vii) G = Set of rational number

Since, the number of elements of set G is infinite.

So, G is an infinite set.