- #1

magnifik

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i have two boolean expressions that I'm simply stuck on. (any variable with the ' mark means NOT). i used http://hopper.unco.edu/KARNAUGH1.1/Function.html" to check my answers for both..apparently they are both supposed to equal 1. i have tried solving the expressions multiple times, and each time i try i get stuck

(A + B)(A' + B + C)(A' + B + C')

= AA' + AB + AC + A'B + BB + BC(A' + B + C')

= AB + AC + A'B + B + BC(A' + B + C')

= B(A + A') + AC + B + BC(A' + B + C')

= B + AC + B + BC(A' + B + C')

= (B + AC + BC)(A' + B + C')

= A'B + BB + BC' + A'AC + BAC + ACC' + A'BC + BBC + BCC'

= A'B + B + BC' + ABC + A'BC + BBC

= A'B + B + BC' + ABC + A'BC + BC

= A'B + B + BC(A + A') + B(C + C')

= A'B + B + BC + B

= B(A' + 1 + C + 1)

= B(A' + C + 1) = A'B + BC + B

need help after this

A + ABC + A'BC + A'B + DA + DA'

= A + BC(A + A') + A'B + D(A + A') by distributive property

= A + BC + A'B + D by complement (A + A' = 1)

i don't know what to do after this...

(A + B)(A' + B + C)(A' + B + C')

= AA' + AB + AC + A'B + BB + BC(A' + B + C')

= AB + AC + A'B + B + BC(A' + B + C')

= B(A + A') + AC + B + BC(A' + B + C')

= B + AC + B + BC(A' + B + C')

= (B + AC + BC)(A' + B + C')

= A'B + BB + BC' + A'AC + BAC + ACC' + A'BC + BBC + BCC'

= A'B + B + BC' + ABC + A'BC + BBC

= A'B + B + BC' + ABC + A'BC + BC

= A'B + B + BC(A + A') + B(C + C')

= A'B + B + BC + B

= B(A' + 1 + C + 1)

= B(A' + C + 1) = A'B + BC + B

need help after this

A + ABC + A'BC + A'B + DA + DA'

= A + BC(A + A') + A'B + D(A + A') by distributive property

= A + BC + A'B + D by complement (A + A' = 1)

i don't know what to do after this...

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