True or false question
If B is a subset of A then {B} is an element of power set A.
I think this is true.
Because B is {1,2} say A {1,2,3} then power set of includes
$\{\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{3,2\},\{1,2,3\},\emptyset\}$
Unless {B} means $\{\{1,2\}\}$
Best Answer
It is true that $B$ is in the power set of a set $A$ (we'll call the powerset $P(A)$) is the set of all subsets of $A$, so the elements of $P(A)$ include all subsets of $A$.
Since $B$ is given to be a subset of $A$, then it is an element in the powerset of $A$.
However, $\{B\}$ is a set containing the subset $B$ as its only element, and so $\{B\}$ is not in the powerset of $A$.