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In Boolean algebra, the consensus theorem or rule of consensus is the identity:

The consensus or resolvent of the terms x y {\displaystyle xy} and x ¯ z {\displaystyle {\bar {x}}z} is y z {\displaystyle yz}. 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. If y {\displaystyle y} includes a term which is negated in z {\displaystyle z} , the consensus term y z {\displaystyle yz} is false; in other words, there is no consensus term.

The conjunctive dual of this equation is:

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