Noun
consensus theorem
(logic) The following theorem of Boolean algebra:
X
Y
+
X
′
Z
+
Y
Z
=
X
Y
+
X
′
Z
{\displaystyle XY+X'Z+YZ=XY+X'Z}
where
Y
Z
{\displaystyle YZ}
, the algebraically redundant term, is called the "consensus term", or its dual form
(
X
+
Y
)
(
X
′
+
Z
)
(
Y
+
Z
)
=
(
X
+
Y
)
(
X
′
+
Z
)
{\displaystyle (X+Y)(X'+Z)(Y+Z)=(X+Y)(X'+Z)}
, in which case
Y
+
Z
{\displaystyle Y+Z}
is the consensus term. (Note:
X
+
Y
,
X
′
+
Z
⊢
Y
+
Z
{\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).)