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) Given set is infinite since infinite parallel rays can be drawn parallel to x-axis.

(ii) Given set is finite since number of letters in English alphabet is 26 which is finite.

(iii) Given set is infinite, since there are many multiples of 5 as {5,10,15,20........}

(iv) Given set is finite, since animals on the Earth are countable.

(v) Given set is infinite, since infinite circles can be drawn from origin (0,0).