No, it is not true that ∅ ∈ ∅.
Explanation:
The empty set, denoted by ∅, is the set containing no elements. In other words, it is a set where nothing is inside. The expression ∅ ∈ ∅ would mean that the empty set is an element of itself. Since the empty set contains no elements, it cannot contain itself.
Analogy:
Think of a completely empty box. The box represents the empty set. For ∅ ∈ ∅ to be true, the empty box would have to contain another empty box inside of it. But since the box is empty, it cannot contain anything, including another empty box.
Formal Definition:
A set A is a member (element) of a set B, denoted A ∈ B, if A is one of the objects that are in the set B. The empty set has no objects in it. Therefore, it can't be a member of itself.
In Summary:
The statement ∅ ∈ ∅ is false because the empty set, by definition, contains no elements, including itself.
