consensus theorem

English

Noun

consensus theorem

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