Consensus theorem

English

Noun

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