Not necessarily. The odd integers and the even integers are two infinitely large sets. But their intersection is the null (empty) set.
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No, because the intersection of two equivalent sets will have a union the same size as its intersection.
The intersection of two sets S and T is the set of all elements that belong to both S and T.
That is called the intersection of the sets.
The set of elements that are elements of the two (or more) given sets is called the intersection of the sets.
You need two sets to have an intersection. If you have two sets, call them R and S, then their intersection is the set T that contains all elements of R that also belong to S OR all elements of S and also belong to R...it's the same thing.