Question

write all the subsets of set phi​

Answer 1

Answer:

only this is the subset of phi = { }

Answer 2

Answer:

. If by ‘phi’ you mean the empty set, then it is a subset of every set, including itself, as a consequence of the underlying logic, which is classical.

So, the standard way of dealing with the usual material conditional holds. And it says that whenever the antecedent of a conditional is false, then the whole conditional is true.

Thus, take first the definition of subset: it says that the set A is a subset of the set B if and only if every element of A is an element of B.

Now, take A being your ‘phi’. Since it has not elements (by definition), the antecedent of the conditional “if x belongs to ‘phi’, then it belongs to B’ is false, hence the whole comdional is true, independently of what is B. And B can be ‘phi’ itself, for nothing impedes that.