simplify the expression
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LHS: ab + (ac)' + ab'c(ab+c)
Apply Demorgan's Law: (ac)' = a' + c'.
= ab + a' + c' + ab'c
= (ab+ab'c) + (a'+c')
= a(b+b'c) + (a'+c')
Apply the dual of distributive law: (b+b'c) = (b+b')(b+c)
= a(b+b')(b+c) + (a'+c')
= ab + ac + a' + c'
= (ab+a') + (ac+c')
= (a+a')(b+a') + (a+c')(c+c')
= b+a'+a+c'
= b+(a'+a)+c'
= b+c'+1 = 1 = RHS
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