How do you simplify (A∩B∩C) ∪ (A∩Bc)∩C) ∪ (A∩Bc∩Cc)?
How would you simplify this using set or boolen algebra ?
(A∩B∩C) ∪ (A∩Bc∩C) ∪ (A∩Bc∩Cc)
Note: the little c is for compliment
thanks :)
More Questions From This User See All
How would you simplify this using set or boolen algebra ?
(A∩B∩C) ∪ (A∩Bc∩C) ∪ (A∩Bc∩Cc)
Note: the little c is for compliment
thanks :)
Copyright © 2024 1QUIZZ.COM - All rights reserved.
Answers & Comments
Verified answer
(A∩B∩C) = (A∩C∩B) and (A∩Bc∩C) = (A∩C∩Bc), so:
(A∩B∩C) ∪ (A∩Bc∩C) = (A∩C∩B) ∪ (A∩C∩Bc) = (A∩C) ∩ (B∪Bc)
= A∩C
So:
(A∩B∩C) ∪ (A∩Bc∩C) ∪ (A∩Bc∩Cc) = A∩C ∪ (A∩Bc∩Cc)
= A ∩ [C∪ (Bc∩Cc) ] = A ∩ [ (C∪Bc) ∩ (C∪Cc) ]
= A ∩ (C∪Bc)
You could also write (A∩C) ∪ (A∩Bc)