State whether each of the following set is finite or infinite:

(i) The set of lines which are parallel to the x-axis.

(ii) The set of letters in the English alphabet.

(iii) The set of numbers which are multiple of 5.

(iv) The set of animals living on the earth.

(v) The set of circles passing through the origin (0,0).

(i) Given: The set of lines which are parallel to the x-axis.

As we know set is a collection of well defined objects.

Let we represent the set in set builder form:

⇒ S = {x:x is number of parallel lines to x-axis}.

Because the set of lines parallel to x-axis are infinite in number. Hence, I t is an infinite set.

(ii) Given: The set of letters in the English alphabet.

As we know set is a collection of well defined objects.

Let we represent the set in roaster form:

⇒ The set of letters in the English alphabet = {A,B,C,…,Z}.

Because the set contain finite alphabet series and having 26 element. Hence, it is a finite set.

(iii) Given: The set of numbers which are multiple of 5

As we know set is a collection of well defined objects.

Let we represent the set in roaster form:

⇒ The set of numbers which are multiple of 5 = {5,10,15,…}.

Because the set contain infinite numbers which are multiple of 5.Hence, it is an infinite set.

(iv) Given: The set of animals living on the earth.

As we know set is a collection of well defined objects.

Let we represent the set in set builder form:

⇒ S = {x:x is the set of animals living on the earth}.

Because the number of animal living on earth are though too large but they are finite in number. Hence, It is finite set.

(v) Given: The set of circles passing through the origin (0,0).

As we know set is a collection of well defined objects.

Let we represent the set in set builder form:

⇒ S = {x:x is the set of circles passing through the origin (0,0)}.

Because the number of circles passing through the origin are infinite in number. Hence, It is an infinite set.