Question

Find the cardinality of ---

1)   $\phi$

2)  { $\phi$}

3)  { $\phi$ ,  { $\phi$} }

4)  { $\phi$,  { $\phi$} , { $\phi$, { $\phi$ } } }

Answer 1

∅=empty set.

{∅}=set which contains ∅ as element.

{ ∅ , {∅} } =set which contains ∅ and {∅} as element.

{ ∅ , {∅}, {∅ , {∅} } } = set which contains ∅ , {∅} and {∅ , {∅} } as element.

Hence,

1)   $\phi$    $\Rightarrow$ Cardinality=0

2)  { $\phi$}   $\Rightarrow $Cardinality=1

3)  { $\phi$ ,  { $\phi$} }   $\Rightarrow$ Cardinality=2

4)  { $\phi$,  { $\phi$} , { $\phi$, { $\phi$ } } }  $\Rightarrow $ Cardinality=3