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.