Empty Set: The empty set (or null set) is a set that has no members. Notation: The symbol ∅ is used to represent the empty set, { }. Note: {∅} does not symbolize the empty set; it represents a set that contains an empty set as an element and hence has a cardinality of one. Equal Sets.

ANSWER: No. The empty set is a subset of every set, including itself, but it is only the element of a set S if S is defined yon such a way as to include the empty set as an element.

A set is a subset of itself since a set contains all its elements. Also, the empty set is a subset of every set, because every element in the empty set belongs to any set since the empty set has no elements.

The empty set i.e phi is a proper subset of any set with at least one element in it and improper subset of phi itself.

The empty set has just 1 subset: 1. A set with one element has 1 subset with no elements and 1 subset with one element: 1 1.

A proper subset is a subset that is not identical to the original set—it contains fewer elements. You can see that there are 16 subsets, 15 of which are proper subsets.

Any Set that does not contain any element is called the empty or null or void set. The symbol used to represent an empty set is – {} or φ. Examples: Let A = {x : 9 < x < 10, x is a natural number} will be a null set because there is NO natural number between numbers 9 and 10.

Any grouping of elements which satisfies the properties of a set and which has at least one element is an example of a non-empty set, so there are many varied examples. The set S= {1} with just one element is an example of a nonempty set. S so defined is also a singleton set. The set S = {1,4,5} is a nonempty set.