Proof: A is a Subset of B iff B' is Subset of A' | Set Theory, Subsets, Set Complement

Let A and B be two subsets of a third set S. Then A is a subset of B if any only if B’ is a subset of A’. We write B’ to indicate the complement of B, which in this context is the set of elements in S but not in B. We would call S the universal set.

We will prove this biconditional result in today’s set theory lesson. It’s a simple proof and both directions are practically the same, using simple definitions of subsets and set complements.



I hope you find this video helpful, and be sure to ask any questions down in the comments!

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