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I am a begginer in progamming language. I have a qusestion which is:
is the empty set an element of every set

Please help me to understand this.

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The set A is a subset of the set B if and only if every element of A is also an element of B.
If A is the empty set then A has no elements and so all of its elements (there are none) belong to B no matter what set B we are dealing with.
That is, the empty set is a subset of every set.Another way of understanding it is to look at intersections. 
The intersection of two sets is a subset of each of the original sets. So if {} is the empty set and A is any set then {} intersect A is {} which means {} is a subset of A and {} is a subset of {}.
You can prove it by contradiction. Let's say that you have the empty set {} and a set A. 
Based on the definition, {} is a subset of A unless there is some element in {} that is not in A. 
So if {} is not a subset of A then there is an element in {}. 
But {} has no elements and hence this is a contradiction, so the set {} must be a subset of A.
An example with an empty set and a non-empty set might be this: the (set of all women who have walked on the moon) and the (set of all astronauts). Examine the three arguments above with this example in mind.


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