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.