Logical Operators, Element-wise & | ~ (MATLAB Functions)

Element-wise logical operations on arrays

Syntax

```
A & B
A | B
~A
```

Description

The symbols &, |, and ~ are the logical array operators AND, OR, and NOT. They work element-by-element on arrays, with 0 representing logical false (F), and anything nonzero representing logical true (T). The logical operators return a logical array with elements set to true (1) or false (0), 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

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

&
Element-wise AND

|
Element-wise OR

&&
Short-circuit AND

||
Short-circuit OR
Lowest

Operator	Operation	Priority
`~`	`NOT`	Highest
`&`	Element-wise `AND`
`\|`	Element-wise `OR`
`&&`	Short-circuit `AND`
`\|\|`	Short-circuit `OR`	Lowest

Remarks

MATLAB always gives the & operator precedence over the | operator. Although MATLAB typically evaluates expressions from left to right, the expression a|b&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 M-file function equivalents, as shown.

Logical Operation
Equivalent Function

A & B
and(A,B)

A | B
or(A,B)

~A
not(A)

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:

u = [0 0 1 1 0 1];
v = [0 1 1 0 0 1];
u | v

ans =
   0   1   1   1   0   1

See Also

all, any, find, logical, xor, true, false

Logical Operators, Short-circuit: &&, ||

Relational Operators: <, <=, >, >=, ==, ~=

Relational Operators < > <= >= == ~= Logical Operators, Short-circuit && ||