# Logic

##### Logical Operators

These operators act on raw, logical and number-like vectors.

- Keywords
- logic

##### Usage

```
! x
x & y
x && y
x | y
x || y
xor(x, y)
```isTRUE(x)

##### Arguments

##### Details

`!`

indicates logical negation (NOT).

`&`

and `&&`

indicate logical AND and `|`

and `||`

indicate logical OR. The shorter form performs elementwise
comparisons in much the same way as arithmetic operators. The longer
form evaluates left to right examining only the first element of each
vector. Evaluation proceeds only until the result is determined. The
longer form is appropriate for programming control-flow and typically
preferred in `if`

clauses.

`xor`

indicates elementwise exclusive OR.

`isTRUE(x)`

is an abbreviation of `identical(TRUE, x)`

, and
so is true if and only if `x`

is a length-one logical vector
whose only element is `TRUE`

and which has no attributes (not even
names).

Numeric and complex vectors will be coerced to logical values, with
zero being false and all non-zero values being true. Raw vectors are
handled without any coercion for `!`

, `&`

, `|`

and
`xor`

, with these operators being applied bitwise (so `!`

is
the 1s-complement).

The operators `!`

, `&`

and `|`

are generic functions:
methods can be written for them individually or via the
`Ops`

(or S4 `Logic`

, see below)
group generic function. (See `Ops`

for
how dispatch is computed.)

`NA`

is a valid logical object. Where a component of
`x`

or `y`

is `NA`

, the result will be `NA`

if the
outcome is ambiguous. In other words `NA & TRUE`

evaluates to
`NA`

, but `NA & FALSE`

evaluates to `FALSE`

. See the
examples below.

See Syntax for the precedence of these operators: unlike many other languages (including S) the AND and OR operators do not have the same precedence (the AND operators have higher precedence than the OR operators).

##### Value

For `!`

, a logical or raw vector(for raw `x`

) of the same
length as `x`

: names, dims and dimnames are copied from `x`

,
and all other attributes (including class) if no coercion is done.

For `|`

, `&`

and `xor`

a logical or raw vector. If
involving a zero-length vector the result has length zero. Otherwise,
the elements of shorter vectors are recycled as necessary (with a
`warning`

when they are recycled only *fractionally*).
The rules for determining the attributes of the result are rather
complicated. Most attributes are taken from the longer argument, the
first if they are of the same length. Names will be copied from the
first if it is the same length as the answer, otherwise from the
second if that is. For time series, these operations are allowed only
if the series are compatible, when the class and `tsp`

attribute of whichever is a time series (the same, if both are) are
used. For arrays (and an array result) the dimensions and dimnames
are taken from first argument if it is an array, otherwise the second.

For `||`

, `&&`

and `isTRUE`

, a length-one logical vector.

##### Note

The elementwise operators are sometimes called as functions as
e.g.``&`(x, y)`

: see the description of how
argument-matching is done in `Ops`

.

##### S4 methods

`!`

, `&`

and `|`

are S4 generics, the latter two part
of the `Logic`

group generic (and
hence methods need argument names `e1, e2`

).

##### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
*The New S Language*.
Wadsworth & Brooks/Cole.

##### See Also

`any`

and `all`

for OR and AND on many scalar
arguments.

`Syntax`

for operator precedence.

`bitwAnd`

for bitwise versions for integer vectors.

##### Examples

`library(base)`

```
# NOT RUN {
y <- 1 + (x <- stats::rpois(50, lambda = 1.5) / 4 - 1)
x[(x > 0) & (x < 1)] # all x values between 0 and 1
if (any(x == 0) || any(y == 0)) "zero encountered"
## construct truth tables :
x <- c(NA, FALSE, TRUE)
names(x) <- as.character(x)
outer(x, x, "&") ## AND table
outer(x, x, "|") ## OR table
# }
```

*Documentation reproduced from package base, version 3.4.3, License: Part of R 3.4.3*