# false

Logical 0 (false)

## Syntax

• `false` example
• `F = false(n)` example
• `F = false(sz)` example
• `F = false(sz1,...,szN)` example
• `F = false(___,'like',p)` example

## Description

example

``false` is shorthand for `logical``(0)`.`

example

````F = false(n)` is an `n`-by-`n` array of logical zeros.```

example

````F = false(sz)` is an array of logical zeros where the size vector, `sz`, defines `size(F)`. For example, ```false([2 3])``` returns a 2-by-3 array of logical zeros.```

example

````F = false(sz1,...,szN)` is a `sz1`-by-`...`-by-`szN` array of logical zeros where `sz1,...,szN` indicates the size of each dimension. For example, `false(2,3)` returns a 2-by-3 array of logical zeros.```

example

````F = false(___,'like',p)` returns an array of logical zeros of the same sparsity as the logical variable `p` using any of the previous size syntaxes.```

## Examples

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### Generate Square Matrix of Logical Zeros

Use `false` to generate a 3-by-3 square matrix of logical zeros.

```A = false(3) class(A)```
```A = 0 0 0 0 0 0 0 0 0 ans = logical```

The result is of class `logical`.

### Generate Array of Logical Zeros with Arbitrary Dimensions

Use `false` to generate a 3-by-2-by-2 array of logical zeros.

`false(3,2,2)`
```ans(:,:,1) = 0 0 0 0 0 0 ans(:,:,2) = 0 0 0 0 0 0```

Alternatively, use a size vector to specify the size of the matrix.

`false([3 2 2])`
```ans(:,:,1) = 0 0 0 0 0 0 ans(:,:,2) = 0 0 0 0 0 0```

Note that specifying multiple vector inputs returns an error.

### Execute Logic Statement

`false` along with `true` can be used to execute logic statements.

Test the logical statement $~\left(A\text{\hspace{0.17em}}\text{​}and\text{\hspace{0.17em}}B\right)\equiv \left(~A\right)or\left(~B\right)$ for A = logical false and B = logical true.

`~(false & true) == (~false) | (~true)`
```ans = 1 ```

The result is logical 1 (true), since the logical statements on both sides of the equation are equivalent. This logical statement is an instance of De Morgan's Law.

### Generate Logical Array of Selected Sparsity

Generate a logical array of the same data type and sparsity as the selected array.

```A = logical(sparse(5,3)); whos A F = false(4,'like',A); whos F```
``` Name Size Bytes Class Attributes A 5x3 41 logical sparse Name Size Bytes Class Attributes F 4x4 49 logical sparse ```

The output array F has the same `sparse` attribute as the specified array A.

## Input Arguments

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### `n` — Size of square matrixinteger

Size of square matrix, specified as an integer. `n` sets the output array size to `n`-by-`n`. For example, `false(3)` returns a 3-by-3 array of logical zeros.

• If `n` is `0`, then `F` is an empty matrix.

• If `n` is negative, then it is treated as `0`.

Data Types: `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

### `sz` — Size vectorrow vector of integers

Size vector, specified as a row vector of integers. For example, ```false([2 3)]``` returns a 2-by-3 array of logical zeros.

• If the size of any dimension is `0`, then `F` is an empty array.

• If the size of any dimension is negative, then it is treated as `0`.

• If any trailing dimensions greater than `2` have a size of `1`, then the output, `F`, does not include those dimensions.

Data Types: `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

### `sz1,...,szN` — Size inputscomma-separated list of integers

Size inputs, specified by a comma-separated list of integers. For example, `false(2,3)` returns a 2-by-3 array of logical zeros.

• If the size of any dimension is `0`, then `F` is an empty array.

• If the size of any dimension is negative, then it is treated as `0`.

• If any trailing dimensions greater than `2` have a size of `1`, then the output, `F`, does not include those dimensions.

Data Types: `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

### `p` — Prototypelogical variable

Prototype, specified as a logical variable.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

## Output Arguments

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### `F` — Output of logical zerosscalar | vector | matrix | N-D array

Output of logical zeros, returned as a scalar, vector, matrix, or N-D array.

Data Types: `logical`

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### Tips

• `false(n)` is much faster and more memory efficient than `logical(zeros(n))`.