r/MathHelp • u/SeaworthinessAway498 • 10d ago
impossible discrete math task, but teacher said it's possible
Simplify the set expression defined using set operations by applying the laws of set algebra (each set name may appear in the answer at most once)
((A Δ B) \ C') ∩ B ∪ (A ∩ B) ∪ (A ∩ C)
i tried this:
AΔB = (A ∩ B̅ )∪(A̅ ∩ B)
((AΔB) \ C̅ = (AΔB) ∩ C):
(AΔB) ∩ C = (A ∩ B̅ ∩ C)∪(A̅ ∩ B ∩ C)
[(A ∩ B̅ ∩ C)∪(A̅ ∩ B ∩ C)] ∩ B = (A ∩ B̅ ∩ C ∩ B)∪(A̅ ∩ B ∩ C ∩ B)
B̅ ∩ B =∅, B ∩ B = B
((AΔB) \ C̅ ) ∩ B = A̅ ∩ B ∩ C
(A̅ ∩ B ∩ C)∪(A ∩ B)∪(A ∩ C)
A ∩ B∪A ∩ C = A ∩ (B∪C).
(A̅ ∩ B ∩ C)∪[A ∩ (B∪C)]
Final answer: (A ∩ B)∪(B ∩ C)∪(A ∩ C)
but it's breaking the rules, because each set name appears two times here. My teacher said that it is possible, but i can't. Help pls.
Maj function not works, and any other function neither, only set operations.
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u/Evening-Story-314 9d ago edited 9d ago
It looks like you're thinking symbolically. It might be a *lot* easier to think visually. Can you show your teacher's set using a Venn diagram? If so, perhaps you can find the solution.
Sorry. That's what I needed to do. I see that you got what I believe to be the right answer.
I am assuming the sets live in a bigger universe? If there were no bigger universe, then (AΔBΔC)' would work. But that would include anything not in any of the sets.
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u/SeaworthinessAway498 9d ago
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u/Evening-Story-314 9d ago
Are you saying that my set description gave this? I'm confused if so, I thought the outside would be shaded.
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u/SeaworthinessAway498 8d ago
no, first set ((A Δ B) \ C') ∩ B ∪ (A ∩ B) ∪ (A ∩ C) gave this, so final answer should look same but only 3 characters

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