Subjective Type

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)

Solution

(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.

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