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# false

Logical 0 (false)

## 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