Question

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

(vii) $\left\{x:xisavowelintheword\text{'}MATHEMATICS\text{'}\right\}$

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 a limited number of vowels in the word ‘MATHEMATICS’ so $\left\{x:xisavowelintheword\text{'}MATHEMATICS\text{'}\right\}$ is a finite set.

Let $A=$$\left\{x:xisavowelintheword\text{'}MATHEMATICS\text{'}\right\}$$=\left\{M,A,T,H,E,I,C,S\right\}$

Hence , The cardinal number for $A=n\left(A\right)=8$