Empty set is proper subset of all universal set true or false.
True
False. The empty set is a subset of every set, but it is not considered a proper subset of any set, including the universal set. By definition, a proper subset must contain at least one element that is not in the original set. Since the empty set has no elements, it cannot be a proper subset of any set.
False. An empty set is not a proper subset of any set, including the universal set.
To understand why this is the case, let's first define what a proper subset is. A proper subset of a set A is a subset that contains some, but not all, elements of A. In other words, if B is a proper subset of A, then all elements of B are also elements of A, and there is at least one element in A that is not in B.
Now, let's consider the empty set, denoted by {}. The empty set has no elements, so it does not contain any elements of the universal set or any other set. Therefore, it cannot be a proper subset of any set, including the universal set.
In conclusion, the statement "Empty set is a proper subset of all universal sets" is false. The empty set is not a proper subset of any set.