化简:(A-B-C)∪((A-B)∩C)∪(A∩B-C)∪(A∩B∩C)

2024-12-01 08:22:39
推荐回答(1个)
回答1:

 ((A-B)-C)∪((A-B)∩C)∪((A∩B)-C)∪(A∩B∩C)
  = ((A∩~B)∩~C)∪((A∩~B)∩C)∪((A∩B)∩~C)∪(A∩B∩C)
  = (A∩(~B∩~C))∪(A∩(~B∩C))∪(A∩(B∩~C))∪(A∩B∩C)
  = A∩((~B∩~C)∪(~B∩C)∪(B∩~C)∪(B∩C))
  = A∩((~B∩(~C∪C))∪(B∩(~C∪C)))
  = A∩(~B∪B)
  = A