consensus theorem

Noun

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