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boolean-logicboolean-expression

Boolean algabra

I'm working on some logic homework and I can't figure out the next step in reducing the number of literals. Any help would be greatly appreciated.

(A + B + C) (A’B’ + C)

A’B’C + AC + BC + C

C(A’B’ + A + B + C)

C((A + B)’ + A + B + C)

I'm pretty sure I use the associative law next, but I don't understand how the not operator is distributed when rearranging.

Solution

  • From the point where you left:

    C((A + B)’ + A + B + C)
C(1 + C)                   ; X' + X = 1 applied to X = A + B
C(1)                       ; 1 + <anything> = 1
C                          ; <anything>1 = <anything>