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Please Help With Boolean Algebra?

I have a test today and I just did some questions on simplifying using boolean theorem and I wanna know if I'm doing them right.

1. (A+B)(C+D)+(AB)+(CD)

2. ((āb)+a)((a+b)+b)

3. (AB+C)+(ABC)

1 Answer

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  • 7 years ago
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    1. (A+B)(C+D)+(AB)+(CD)

    = (A+B)C + (A+B)D + (AB) + (CD)

    = (AC)+(BC)+(AD)+(BD) + (AB) + (CD)

    2. ((āb)+a)((a+b)+b)

    = ((āb)+a)(a + (b+b))

    = ((āb)+a)(a + b)

    = ((āb)+a)a + ((āb)+a)b

    = (āb)a + aa + (āb)b + ab

    = b(āa) + a + ā(bb) + ab

    = b(false) + a + āb + ab

    = false + a + (ā + a)b

    = a + (true)b

    = a + b

    3. (AB + C) + ABC

    = (AB + ABC) + C

    = (AB(true) + ABC) + C

    = AB(true + C) + C

    = AB(true) + C

    = AB + C

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