Question

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) 

Answer 1

(i) The set of lines which are parallel to the x-axis is an infinite set because lines parallel to the x-axis are infinite in number. 

(ii) The set of letters in the English alphabet is a finite set because it has 26 elements. 

(iii) The set of numbers which are multiple of 5 is an infinite set because multiples of 5 are infinite in number. 

(iv) The set of animals living on the earth is a finite set because the number of animals living on the earth is finite (although it is quite a big number). 

(v) The set of circles passing through the origin (0, 0) is an infinite set because infinite number of circles can pass through the origin.