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8.5.1 Elementbyelement Boolean Operators
An elementbyelement boolean expression is a combination of comparison expressions using the boolean operators “or” (‘’), “and” (‘&’), and “not” (‘!’), along with parentheses to control nesting. The truth of the boolean expression is computed by combining the truth values of the corresponding elements of the component expressions. A value is considered to be false if it is zero, and true otherwise.
Elementbyelement boolean expressions can be used wherever comparison
expressions can be used. They can be used in if
and while
statements. However, a matrix value used as the condition in an
if
or while
statement is only true if all of its
elements are nonzero.
Like comparison operations, each element of an elementbyelement boolean expression also has a numeric value (1 if true, 0 if false) that comes into play if the result of the boolean expression is stored in a variable, or used in arithmetic.
Here are descriptions of the three elementbyelement boolean operators.

boolean1 & boolean2

Elements of the result are true if both corresponding elements of boolean1 and boolean2 are true.

boolean1  boolean2

Elements of the result are true if either of the corresponding elements of boolean1 or boolean2 is true.

! boolean

~ boolean

Each element of the result is true if the corresponding element of boolean is false.
For matrix operands, these operators work on an elementbyelement basis. For example, the expression
[1, 0; 0, 1] & [1, 0; 2, 3] 
returns a two by two identity matrix.
For the binary operators, the dimensions of the operands must conform if both are matrices. If one of the operands is a scalar and the other a matrix, the operator is applied to the scalar and each element of the matrix.
For the binary elementbyelement boolean operators, both subexpressions boolean1 and boolean2 are evaluated before computing the result. This can make a difference when the expressions have side effects. For example, in the expression
a & b++ 
the value of the variable b is incremented even if the variable a is zero.
This behavior is necessary for the boolean operators to work as described for matrixvalued operands.
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