yes
Yes.
I was told once that the null set is the compliment to the universal set... I'm not convinced of this, however because the null set is a subset of the universal set as well. While I can't think of anything offhand that would prevent both of these statements from being true, it seems to me that they are contradictory statements.
Universal set.
The complement of an empty set is universal set
Yes. A null set is always a subset of any set. Also, any set is a subset of the [relevant] universal set.
The complement of a set refers to the elements that are not included in that set but are part of a larger universal set. For example, if the universal set is all natural numbers and set A consists of even numbers, the complement of set A would be all the odd numbers within the universal set. Mathematically, the complement of set A is often denoted as A'.
The null set. It is a subset of every set.
null set ,universal set,cardinality set
An absolute complement is the set which includes exactly the elements belonging to the universal set but not to a given set.
The complement of a set S, relative to the universal set U, consists of all elements of U that are not in S.
The complement of a set consists of all elements in the universal set that are not in the given set. If the set is denoted as A, its complement is often represented as A' or A^c. For example, if the universal set U contains elements {1, 2, 3, 4, 5} and set A contains {2, 3}, then the complement of A would be {1, 4, 5}. The complement effectively highlights what is excluded from the specified set.
a set which has no elements in it is called a null set. example - A={}.