Question

1. State whether the following sets are empty, finite or infinite sets. In case of (non-empty) finite sets, mention the cardinal number.

(i) $\left\{allcoloursofarainbow\right\}$

Answer 1

Empty sets: A set that contains no elements is called an Empty set.

Finite sets: A set that contains a limited (countable) number of different elements is called a Finite set.

Infinite sets: A set that contains an unlimited (uncountable) number of different elements is called an Infinite set.

There are seven colours in a rainbow which is countable in number so $\left\{allcoloursofarainbow\right\}$ is a Finite set.

$\left\{allcoloursofarainbow\right\}$$=\left\{Voilet,Indigo,Blue,Green,Yellow,Orange,Red\right\}$

The cardinal number represents the number of elements in any set. So the cardinal number for the given set $\left\{Voilet,Indigo,Blue,Green,Yellow,Orange,Red\right\}$ is $n\left(allcoloursofarainbow\right)=7$