Element-Chasing Proofs Discussion

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

Element chasing, or “choose an element” proofs, are a common way to prove equality or subset relationships between sets. This discussion offers a chance to try this idea by completing Progress Check 5.12 from our textbook. In particular…

Discuss how you would prove the equality

where A and B are sets, both being subsets of some universal set U. You might, for example, offer suggestions for how you would start the proof, what it’s overall strategy and structure could be, examples of particular sets that illustrate what the claim is saying, ideas for building on previous posts, etc.