consensus theorem

English

consensus theorem

(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 ${\\displaystyle \eg }$ might make this more evident).)

单词	consensus theorem
释义	consensus theorem English Noun consensus theorem (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 ${\\displaystyle \eg }$ might make this more evident).)
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