AB+AC+BC=AB+AC(Consensus Theorem)
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Answer:
AB + A'C + BC = AB + A'C
AB + A'C + BC = AB + A'CThe consensus or resolvent of the terms AB and A’C is BC. It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other.
AB + A'C + BC = AB + A'CThe consensus or resolvent of the terms AB and A’C is BC. It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other.The conjunctive dual of this equation is:
AB + A'C + BC = AB + A'CThe consensus or resolvent of the terms AB and A’C is BC. It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other.The conjunctive dual of this equation is:(A+B).(A'+C).(B+C) = (A+B).(A'+C)
AB + A'C + BC = AB + A'CThe consensus or resolvent of the terms AB and A’C is BC. It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other.The conjunctive dual of this equation is:(A+B).(A'+C).(B+C) = (A+B).(A'+C)In the second line, we omit the third product term BC.Here, the term BC is known as Redundant term. In this way we use this theorem to simply the Boolean Algebra.
Explanation:
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Answer:
ab+a'c+bc
=ab+a'c+bc(a+'a)
(a+'a=1,complimentary law)
ab+a'c+abc+a'bc
=ab+abc+a'c+a'bc(associative law)
=ab+a'c(absorption law)