State whether the given set is finite or infinite :

(i) Set of all even natural numbers.

(ii) Set of all odd integers.

(iii) Set of all rivers in India.

(iv) Set of all points on a line segment 1 cm long.

(v) Set of all factors of 1200.

(vi) Set of all multiples of 6.

(vii) Set of all drops of water in a bucket.

(i) Set of all even natural numbers.

Natural numbers go on forever (2, 4, 6, 8, …..), so the counting process never ends.

∴ It is an infinite set.

(ii) Set of all odd integers.

Integers extend infinitely in both positive and negative directions (…., -3, -1, 1, 3, ….).

∴ It is an infinite set.

(iii) Set of all rivers in India.

Although there are many rivers, the total number is a specific, countable figure that can be listed.

∴ It is a finite set.

(iv) Set of all points on a line segment 1 cm long.

Mathematically, a line segment consists of an uncountable infinity of points, regardless of its length.

∴ It is an infinite set.

(v) Set of all factors of 1200.

Every number has a limited (finite) number of factors.

∴ It is a finite set.

(vi) Set of all multiples of 6.

Multiples are generated by multiplying 6 by natural numbers (6, 12, 18, ….), which are endless.

∴ It is an infinite set.

(vii) Set of all drops of water in a bucket.

The number is extremely large and difficult to count.

∴ It is an infinite set.