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Which of the ...

Question

Which of the following sets are finite and which are infinite ?

(i) Set of concentric circles in a plane.

(ii) Set of letter of the English Alphabets.

(iii) { $x ϵ N; x > 5$ }

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Solution

(i) Infinite, since with a common centre infinitely many circles can be drawn in a plane.

(ii) Finite, as there are only 26 letters of English Alphabet.

(iii) Infinite, $∵$ { $x ϵ N; x > 5$ } = {6,7,8,.....} which is infinite.

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Similar questions

Which of the following sets are finite and which are infinite ?

(i) Set of concentric circles in a plane.

(ii) Set of letter of the English Alphabets.

(iii) { $x ϵ N; x > 5$ }

(iv) { $x ϵ N; x > 200$ }

(v) { $x ϵ Z; x < 5$ }

(vi) { $x ϵ R; 0 < x < 1$ }.

State whether each of the following sets 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 multiples of 5.

(iv) The set of animals living on the earth.

(v) The set of circles passing through the origin (0, 0).

5

(i)

x -

(i i)

(i i i)

5

(i v)

(v)

(0, 0)

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