Proof:A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (example of poor style)

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Students are often tempted to do proofs about sets by rewriting the logical statements inside the set definitions. Avoid this style for the following reasons:

  • Proving that the logical rewriting steps are justified is usually just as complicated as the proof that the sets are equal
  • This technique doesn't work anymore once we get past very simple examples. We want you to build good habits while working on the simple cases.

Doing computations or rewriting is a good proof technique in general, but we would like you to avoid doing logical rewriting for now.

Instead, you should make use of the definitions and proof technique to give a step-by-step argument for why a given relationship holds.