SOLUTION: Given three sets, A, B and C, use the laws of the algebra on sets to show that (A U B U C) &#8745 (A U B' U C) &#8745 (A U C)' = ∅

Algebra ->  Probability-and-statistics -> SOLUTION: Given three sets, A, B and C, use the laws of the algebra on sets to show that (A U B U C) &#8745 (A U B' U C) &#8745 (A U C)' = ∅      Log On


   

Question 1147276: Given three sets, A, B and C, use the laws of the algebra on sets to show that
(A U B U C) ∩ (A U B' U C) ∩ (A U C)' = ∅
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(A U B U C) ∩ (A U B' U C) = (A U C)

(A U C) ∩ (A U C)' = ∅


Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.

            In the post by @greenestamps,  the first line is not correct.

            So,  I came to bring the correct solution. 


(A U B U C) ∩ (A U B' U C) = ((A\ (A ∩ B)) U (C\ (C ∩ B)).


((A\ (A ∩ B)) U (C\ (C ∩ B)) ∩ (A U C)' = ∅


Here the sign  " \ " denotes the difference of a subset and its sub-subset.


Solved.