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) {$xϵN;x>5$}

(iv) {$xϵN;x>200$ }

(v) {$xϵZ;x<5$ }

(vi) {$xϵR;0<x<1$ }.

Answer 1

(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, $\because$ {$xϵN;x>5$} = {6,7,8,.....} which is infinite.

(iv) Finite, $\because$ $xϵN;x>200$ } = {1, 2,3,....199} which is finite.

(v) Infinite, $\because$ {$xϵZ;x<5$ } = - {......, -3,-2,-1,0,1,2,3,4} which is infinite.

(vi) {$xϵR;0<x<1$ } is an infinite set $\because$ an interval is an infinite set.