Question:
Rewrite the following statements using the set notation:
(i) $\mathrm{a}$ is an element of set $\mathrm{A}$.
(ii) $b$ is not an element of $A$.
(iii) $A$ is an empty set and $B$ is a nonempty set.
(iv) A number of elements in A is 6 .
(v) 0 is a whole number but not a natural number.
Solution:
(i) Given: a is an element of set A
this means a $\in \mathrm{A}$
(ii) Given: $b$ is not an element of $A$
this means $\mathrm{b} \notin \mathrm{A}$
(iii) Given: $A$ is an empty set
and $B$ is a non-empty set
this means $\mathrm{A}=\phi$
and $B \neq \phi$
(iv) Given: In set A, total number of elements is 6
This means, $|\mathrm{A}|=6$
(v) Given: 0 is a whole number but not a natural number
This means 0 ∈ W but 0 ∉ N