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

Free monoid - Wikipedia, the free encyclopedia may mean an alphabet set minus the empty string.

may be the empty string.

Guessing,

may be the 2-tuples of elements of A.

With the above, I further conjucture weakly:

a) is false.

is not a 2-tuple.

b) is false.

is not a 2-tuple.

does not result in

c) not sure what

implies.

d) is true. Removing the empty string twice from the set

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.