Question

State whether each of the following set is finite or infinite:
$\left(i\right)$ The set of lines which are parallel to the $x-$axis
$\left(ii\right)$ The set of letters in the English alphabet
$\left(iii\right)$ The set of numbers which are multiple of $5$
$\left(iv\right)$ The set of animals living on the earth
$\left(v\right)$ The set of circles passing through the origin $(0,0)$

Answer 1

$\left(i\right)\because$ The lines which are parallel to the $x-$axis are infinite, So given set is an infinite set.

$\left(ii\right)$ English alphabet contains $26$ letters $i.e.,26$ elements. So given set is a finite set.

$\left(iii\right)$ The set of multiples of $5=\{5,10,15,20,25,30...\}.$ This set has infinite numbers. So given set is an infinite set.

$\left(iv\right)$ The number of animals living on the earth is a very large number but finite. So, given set is a finite set.

$\left(v\right)$ Since infinite number of circles can pass through the origin. So given set is an infinite set.