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State whether each of the following set ...

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 number 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).

Text Solution

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(i) `because` Infinite lines can be drawn parallel to a given line
`:.` Set of lines which are parallel to the x-axis is finite
(ii) `because` There are 26 letters in English alphabet
Therefore, the set of leters in English alphabet is finite
(iii) `because` Multiplies of 5 = 5, 10, 15,20,....
Therefore, the set of numbers which are multiple of 5 is infinite
(iv) `because` The set of animals living on the earth is finite
Therefore, the set of animals living on the earth is finite
(v) `because` Infinite circles can be drawn passing through origin (0,0)
Therefore, the set of circles passing through the origin (0,0) is infinite.
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