2010/055) Prove ABC+AB'C+ABC'+A'BC=AB+BC+CA by using boolean laws only.

ABC+AB'C+ABC'+A'BC = ABC+AB'C+ABC'+A'BC + ABC + ABC

as ABC + ABC = ABC so we can add 2 copies of ABC

= ABC+AB'C+ABC'+ ABC + A'BC + ABC ( rearranging)
= AC(B+B') + AB(C'+C) + BC(A' + A) ) grouping)
= AC + AB +CA as B+B' = 1 A+A'=1 and C+C'= 1