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).

Answer 1

Given, P(A : B) = set of all those subsets of A which are supersets of B.

$ \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 $]

= P(A)