Proof: A-B is a Subset of A union B | Set Theory

We prove that A-B is a subset of A union B. A-B is set subtraction, but it is also sometimes written as A\B, which is read as the relative complement of B with respect to A. AUB is the union of A and B and just puts the two sets together, as in it contains all elements from A and all elements from B.

We can think of A-B as beginning with A and then taking all elements from B out of A. We can think of A\B as beginning with B, and then taking the set of all elements not in B that are in A. Either way, we end in the same place, with a set that has all elements of A that are not in B.

To prove A-B is a subset of A union B, we just prove that if an element is in A-B then it must be in A union B as well, which we'll see is quite easy when we apply our definitions!

What is a Union? What is a Union? (Set Theory)
What is Set Subtraction? What is Set Subtraction?

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