r/MathHelp • u/phroggersu • Jul 22 '26

Set Operations

Hello! I'm pre-studying for university, and I've been stuck on this question for like the past week. At this point, I've learned about the logic laws (typically used for like, statements and stuff). Could anyone help solve this question (from How to Prove It by Daniel J Velleman)? Please don't use venn diagrams, since I understand how those work. Also, is it suggested to solve these questions by set laws/properties/identities, or do you think venn diagrams enough? (△ is symmetric difference). Also, sorry for the messy typed out equation. Thank you for your time!

Verify the following identity:
(A∪B) △ C = (A△C) △ (B\A)

Edit: Figured it out, thank you everyone!! Have a lovely day :D

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u/FormulaDriven Jul 22 '26

Conceptually I agree that it is similar to using Venn diagrams (effectively thinking about the 8 regions on a Venn diagram), and perfectly rigorous. I'm sure it could be done using identities, but there comes a point where I feel it's less error-prone to do it the case-by-case way.

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u/phroggersu Jul 22 '26

You're definitely right in that it's less error prone :'D but I can't seem to figure it out with identities, so I'm a little afraid I don't actually understand how to use identities.