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can be written as

For all x, if x is A, then x is B.

If F = {x : x in domain, x is A}

and G = {y : y in domain, y is B}

Then I can write, "For all x, if x is A, then x is B" as

F intersect G = F

Similarly, I can write, "Some A's are B's" as

F intersect G [x=] [null]

I can write, "No A's are B's" as

F intersect G = [null]

I can write, "Only A's are B's" as

F intersect G = G

It seems that this approach might bring about considerale results (if only I knew more about the algebra of sets).

Is there some branch of logic that studies logic in this manner? Or is it simply more convenient to study logic conventionally? What is meant by the term "mathematical logic?"