I am not sure. Doing a wiki search on "alphabet subset theory" I came up with this.

Free monoid - Wikipedia, the free encyclopedia
$\displaystyle V^{*}$ may mean an alphabet set minus the empty string.

$\displaystyle \lambda$ may be the empty string.

Guessing, $\displaystyle A^2$ may be the 2-tuples of elements of A.

With the above, I further conjucture weakly:

a) is false. $\displaystyle A \$ is not a 2-tuple.

b) is false. $\displaystyle A \$ is not a 2-tuple. $\displaystyle A = A^2 \$ does not result in $\displaystyle \ \ \lambda \in A$

c) not sure what $\displaystyle A\{\lambda\}$ implies.

d) is true. Removing the empty string twice from the set $\displaystyle A$ which already does not contain the empty string, is equivalent to removing the empty string once.

Supply more context on the source of this, for example: title of book, paragraph, section or chapter, or class topic under discussion.