Last Updated：2025/11/27
(logic) The following theorem of Boolean algebra: XY+X'Z+YZ=XY+X'Z where YZ, the algebraically redundant term, is called the consensus term
, or its dual form (X+Y)(X'+Z)(Y+Z)=(X+Y)(X'+Z), in which case Y+Z is the consensus term. (Note: X+Y,X'+Z⊢Y+Z is an example of the resolution inference rule (replacing the + with ∨ and the prime with prefix ¬ might make this more evident).)
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consensus theorem
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Source Word
consensus theorem
Noun
(logic)
The
following
theorem
of
Boolean
algebra:
XY+X'Z+YZ=XY+X'Z
where
YZ,
the
algebraically
redundant
term,
is
called
the
"consensus
term",
or
its
dual
form
(X+Y)(X'+Z)(Y+Z)=(X+Y)(X'+Z),
in
which
case
Y+Z
is
the
consensus
term.
(Note:
X+Y,X'+Z⊢Y+Z
is
an
example
of
the
resolution
inference
rule
(replacing
the
+
with
∨
and
the
prime
with
prefix
¬
might
make
this
more
evident).)
Japanese Meaning
コンセンサス定理（合意定理とも呼ばれる）とは、ブール代数における定理で、論理式 XY + X'Z + YZ = XY + X'Z （またはその双対形式 (X+Y)(X'+Z)(Y+Z) = (X+Y)(X'+Z)）が成立することを示す。この定理において、YZ（または Y+Z）は余分な項（コンセンサス項）と呼ばれ、論理式の簡略化に寄与する。
Sense（1）
(logic)
The
following
theorem
of
Boolean
algebra:
XY+X'Z+YZ=XY+X'Z
where
YZ,
the
algebraically
redundant
term,
is
called
the
"consensus
term",
or
its
dual
form
(X+Y)(X'+Z)(Y+Z)=(X+Y)(X'+Z),
in
which
case
Y+Z
is
the
consensus
term.
(Note:
X+Y,X'+Z⊢Y+Z
is
an
example
of
the
resolution
inference
rule
(replacing
the
+
with
∨
and
the
prime
with
prefix
¬
might
make
this
more
evident).)
