not
, _not
Logical negation
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not b
_not(b
)
not b
represents the logical negation of
the Boolean expression b
.
MuPAD^{®} uses a three state logic with the Boolean constants TRUE
, FALSE
,
and UNKNOWN
.
These are processed as follows:
not TRUE = FALSE
not FALSE = TRUE
not UNKNOWN = UNKNOWN
_not(b)
is equivalent to not b
.
Boolean expressions can be composed of these constants as well
as of arbitrary arithmetical expressions. Typically, equations, such
as x = y
, and inequalities, such as x
<> y
, x < y
, and x
<= y
, are used to construct Boolean expressions.
Combinations of the constants TRUE
, FALSE
, UNKNOWN
inside a Boolean
expression are simplified automatically. However, symbolic Boolean
subexpressions, equalities, and inequalities are not evaluated and
simplified by logical operators. Use bool
to evaluate such expressions to
one of the Boolean constants. Note, however, that bool
can evaluate inequalities x
< y
, x <= y
and so on only if they
are composed of numbers of type Type::Real
. See Example 2.
Use simplify
with
the option logic
to simplify expressions involving
symbolic Boolean subexpressions. See Example 3.
The precedences of the logical operators are as follows. If in doubt, use brackets to make sure that the expression is parsed as desired.
The operator not
is stronger binding
than and
, that is, not b1 and b2
= (not
b1) and b2
.
The operator and
is stronger binding
than xor
, that is, b1 and b2 or b3
= (b1
and b2) xor b3
.
The operator xor
is stronger binding
than or
, that is, b1 xor b2 or b3
= (b1
xor b2) or b3
.
The operator or
is stronger binding
than ==>
, that is, b1 or b2 ==>
b3
= (b1 or b2) ==> b3
.
The operator ==>
is stronger
binding than <=>
, that is, b1 ==>
b2 <=> b3
= (b1 ==> b2) <=> b3
.
In the conditional context of if
, repeat
, and while
statements, Boolean expressions
are evaluated via “lazy evaluation” (see _lazy_and
, _lazy_or
). In any other
context, all operands are evaluated.
Combinations of the Boolean constants TRUE
, FALSE
,
and UNKNOWN
are simplified automatically to one
of these constants:
TRUE and not (FALSE or TRUE)
not UNKNOWN
Logical operators simplify subexpressions that evaluate to the
constants TRUE
, FALSE
, UNKNOWN
.
b1 or b2 and (not FALSE)
FALSE or ((not b1) and TRUE)
b1 and (b2 or FALSE) and (not UNKNOWN)
However, equalities and inequalities are not evaluated:
not(x = x) and (1 < 2) and (2 < 3) and (3 > 4)
Boolean evaluation is enforced via bool
:
bool(%)
Expressions involving symbolic Boolean subexpressions are not
simplified by and
, or
, not
.
Simplification has to be requested explicitly via the function simplify
:
(b1 and b2) or (b1 and (not b2)) and (1 < 2)
simplify(%, logic)

Boolean expressions 
Boolean expression.
b
, b_1
, b_2