Home  >>  AIMS  >>  Class11  >>  Math  >>  Sets

# Let B be a subset of A and let P(A : B) = (X $\in$ P(A) : X $\supseteq$ B}. Show that P(A : $\phi$) = P(A).

$\therefore$ P(A = $\phi$) = set of all those subsets of A which are supersets of $\phi$.
= set of all subsets of A [$\because$ every subset of A is a superset of $\phi$]