How many elements has $P(A),$ if $A=\varnothing ?$
How many elements has $P(A),$ if $A=\varnothing ?$
We know that if $A$ is a set with $m$ elements i.e., $n(A)=m,$ then $n[p(A)]=2^{m}$
If $A=\varnothing,$ then $n(A)=0$
$\therefore n[P(A)]=2^{0}=1$
Hence, $P(A)$ has one element.
Similar Questions
Which set is the subset of all given sets
Which set is the subset of all given sets
Write the following sets in the set-builder form :
${\rm{\{ 5,25,125,625\} }}$
Write the following sets in the set-builder form :
${\rm{\{ 5,25,125,625\} }}$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{ \{ 3,4\} \} \subset A$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{ \{ 3,4\} \} \subset A$
Examine whether the following statements are true or false :
$\{ a\} \in \{ a,b,c\} $
Examine whether the following statements are true or false :
$\{ a\} \in \{ a,b,c\} $
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $A \not\subset B$ and $B \not\subset C,$ then $A \not\subset C$
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $A \not\subset B$ and $B \not\subset C,$ then $A \not\subset C$