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The Answerer
Lv 6
The Answerer asked in Science & MathematicsMathematics · 10 years ago

Boolean Algebra Simplification?

Could anyone simplify these logic expressions into sum of product forms?

a. ((ab)'c(a' + (b + c)'))'

b. (((b + c)'+a')'+c)'

1 Answer

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  • Fazaldin A
    Lv 7
    10 years ago
    Favorite Answer

    a).

    ((ab)'c(a' + (b + c)'))' = ((a'c+b'c)(a'+b'c'))' = (a'c+b'c)'+(a'+b'c')

    ((ab)'c(a' + (b + c)'))' = (a+c')(b+c')+a(b+c)

    ((ab)'c(a' + (b + c)'))' = ab+ac'+bc'+c'+ab+ac = ab+c'(a+b+1)+ac

    ((ab)'c(a' + (b + c)'))' = ab+c'+ac = ab+c'+a

    ((ab)'c(a' + (b + c)'))' = a+c' >=================< ANSWER

    b).

    (((b + c)'+a')'+c)' = ((b'c'+a')'+c)' = ((b'c')'a+c)'

    (((b + c)'+a')'+c)' = ((b+c)a+c)' = (ab+ac+c)'

    (((b + c)'+a')'+c)' = (ab+c)' = (ab)'+c'

    (((b + c)'+a')'+c)' = a'+b'+c' >================< ANSWER

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