consensus theorem

{{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).)