(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.