consensus theorem

Fetched 2026-10-26 (cache).

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Proper noun

1. {{lb|en|logic}} The following theorem of [[Boolean algebra]]: <math>XY + X'Z + YZ = XY + X'Z</math> where <math>YZ</math>, the algebraically redundant term, is called the "consensus term", or its dual form <math>(X + Y)(X' + Z)(Y + Z) = (X + Y)(X' + Z)</math>, in which case <math>Y + Z</math> is the consensus term. (''Note'': <math>X+Y, X'+Z \vdash Y+Z</math> is an example of the {{w|Resolution (logic)|resolution}} [[inference rule]] (replacing the <math>+</math> with <math>\vee</math> and the prime with prefix <math>\neg</math> might make this more evident).)

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