Question

Classify the following sets into finite or infinite.
(i) A = {1, 3, 5, 7, ...}
(ii) B = {101, 102, 103, ..., 1000}
(iii) C = {x|x $\in$ Q, 3< x < 5}
(iv) D = {y|y = 3ⁿ, n $\in$ N}

Answer 1

Finite set: A set is called a finite set if has a finite number of elements.

Infinite set: A set is called an infinite set if it has an infinite number of elements.

(i) The given set contains all odd numbers. There are infinite odd numbers. Therefore, it is an infinite set.

(ii) The given set contains all natural numbers starting from 101 to 1000, which is countable. Therefore, it is a finite set.

(iii) The given set contains all rational numbers between 3 and 5. There is an infinite number of rational numbers between 3 and 5. Therefore, it is an infinite set.

(iv) D = { 3¹,3² ,3³,3⁴,...}
The given set contains an infinite number of elements. Therefore, it is an infinite set.