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It isn't! The greek letter phi (φ) can mean lots of things in mathematics, but not what you're thinking. The empty set already has a fitting name, which is "the empty set", nothing else. You can represent it unambiguously with a pair of curly brackets: {}.
If you insist, though, there does exist a symbol to represent the empty set: Ø, based off of a letter in the Norwegian alphabet. Note the forward slash instead of the vertical bar. This symbol should never be confused with phi, which might have other uses in the same context.
You probably meant to ask this: Why_is_an_empty_set_a_subset_of_every_set
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What is a different from subset and proper subset?
If set A and set B are two sets then A is a subset of B whose all members are also in set B.
What is the difference between improper subset and equal sets?
There is no difference between improper subset and equal sets. If A is an improper subset of B then A = B. For this reason, the term "improper subset" is rarely used.
Why is it non set is asubset of all sets?
A "subset" means you can make it out of the pieces in the original set. No matter what set you begin with, you always have the option to choose no pieces at all--that creates the null subset.
An example of why any subset can not be a proper subset?
Assume that set A is a subset of set B. If sets A and B are equal (they contain the same elements), then A is NOT a proper subset of B, otherwise, it is.
What is proper sub-set?
A proper subset is a subset that includes some BUT NOT ALL of the elements of the original set. If the subset is finite, its order must be smaller than that of the original set but that need not be the case if the two sets are infinite. For example, even integers are a proper subset of all integers but they both contain an infinite umber of elements.
