MATLAB Function Reference 
Elementwise logical operations on arrays
Syntax
Description
The symbols &
, 
, and ~
are the logical array operators AND
, OR
, and NOT
. They work element by element on arrays, with logical 0
representing false
, and logical 1
or any nonzero element representing true
. The logical operators return a logical
array with elements set to 1
(true
) or 0
(false
), as appropriate.
The &
operator does a logical AND
, the 
operator does a logical OR
, and ~A
complements the elements of A
. The function xor(A,B)
implements the exclusive OR
operation. The truth table for these operators and functions is shown below.
Inputs  and 
or 
not 
xor 

A 
B 
A & B 
A  B 
~A 
xor(A,B) 
0 
0 
0 
0 
1 
0 
0 
1 
0 
1 
1 
1 
1 
0 
0 
1 
0 
1 
1 
1 
1 
1 
0 
0 
The precedence for the logical operators with respect to each other is
Operator 
Operation 
Priority 
~ 
NOT 
Highest 
& 
Elementwise AND 

 
Elementwise OR 

&& 
Shortcircuit AND 

 
Shortcircuit OR 
Lowest 
Remarks
MATLAB always gives the &
operator precedence over the 
operator. Although MATLAB typically evaluates expressions from left to right, the expression ab&c
is evaluated as a(b&c)
. It is a good idea to use parentheses to explicitly specify the intended precedence of statements containing combinations of &
and 
.
These logical operators have Mfile function equivalents, as shown.
Logical Operation 
Equivalent Function 
A & B 
and(A,B) 
A  B 
or(A,B) 
~A 
not(A) 
Examples
This example shows the logical OR
of the elements in the vector u
with the corresponding elements in the vector v
:
See Also
all
, any
, find
, logical
, xor
, true
, false
Logical operators, shortcircuit, &&
, 
Relational operators <
, <=
, >
, >=
, ==
, ~=
logical  Logical Operators: Shortcircuit &&  
© 19942005 The MathWorks, Inc.