Question

I just want to verify a statement ....

Answer 1

is it true that:

If \(\color{black}{{\rm A\subseteq B}}\), then \(\color{black}{\mathscr{P}({\rm A})\subseteq\mathscr{P}({\rm B})}\)?

Answer 2

let's see if I can do an example or two and figure this out ...

\(\color{black}{A=\{1,5\}}\) and \(\color{black}{B=\{1,2,5\}}\).

\(\color{black}{\mathscr{P}(A)=\{\emptyset, 1,5,\{1,5\}\}}\)
\(\color{black}{\mathscr{P}(B)=\{\emptyset, 1,5,\{1,5\}~~\rm~~and~then~all~subsets~containing~«2».\}}\)

Answer 3

Oh, yes, I got my query solved:)