Is empty set super set

Answer 1

No, an empty set can't be the super set.

The definition of super set is as follows:

If A and B are sets, and every element of A is also an element of B, then B is the super set of A, denoted by B ⊇ A.

Another way to interpret this is A ⊆ B, which means that "A is the subset of B".

Suppose that ∅ is the super set. This implies:

∅ ⊇ A [Which is not true! Contradiction!]

Remember that ∅ and {∅} are two different sets. If we have {∅}, then there exists an element that belongs to that set since ∅ is contained in that set. On the other hand, ∅ doesn't have any element, including ∅.

Therefore, an empty set can't be the super set.