The conversation between human and AI assistant.
How do you prove that for all sets A, B and C, (A∪B) \C = (A\C) ∪ (B \C)?
I see, that makes sense. Can you give me an example to illustrate this proof?
Sure. Let's say we have sets A = {1, 2, 3}, B = {3, 4, 5}, and C = {3, 6}. Then we have (A∪B) \C = {1, 2, 4, 5} \ {3, 6} = {1,2,4,5}. And we also have (A\C) ∪ (B\C) = {1,2} ∪ {4,5} = {1,2,4,5}. So we can see that (A∪B) \C = (A\C) ∪ (B\C) in this case.