# consensus theorem

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