# symfalse

Symbolic logical constant false

## Syntax

``symfalse``
``F = symfalse(n)``
``F = symfalse(sz)``
``T = symfalse(sz1,...,szN)``

## Description

example

````symfalse` is the symbolic logical constant for the false condition.```

example

````F = symfalse(n)` returns an `n`-by-`n` matrix of symbolic logical `symfalse`s.```

example

````F = symfalse(sz)` returns an array of symbolic logical `symfalse`s where the size vector, `sz`, defines `size(T)`. For example, `symfalse([2 3])` returns a 2-by-3 array of symbolic logical `symfalse`s.```

example

````T = symfalse(sz1,...,szN)` returns a `sz1`-by-`...`-by-`szN` array of symbolic logical `symfalse`s where `sz1,...,szN` indicates the size of each dimension. For example, `symfalse(2,3)` returns a 2-by-3 array of symbolic logical `symfalse`s.```

## Examples

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Create a symbolic inequality ${x}^{2}>4$.

```syms x eq = x^2 > 4```
`eq = $4<{x}^{2}$`

Assume that $-2.

`assume(-2<x & x<2)`

Simplify the condition represented by the symbolic inequality `eq`. The `simplify` function returns the symbolic logical constant `symfalse` since the condition never holds for the assumption $-2.

`F = simplify(eq)`
`F = $\mathrm{symfalse}$`

Display the data type of `F`, which is `sym`.

`class(F)`
```ans = 'sym' ```

You can also use `isAlways` to check if the inequality does not hold under the assumption being made. In this example, `isAlways` returns logical `0` (`false`).

`TF = isAlways(eq)`
```TF = logical 0 ```

Use `symfalse` to generate a 3-by-3 square matrix of symbolic logical `symfalse`s.

`F = symfalse(3)`
```F =  $\left(\begin{array}{ccc}\mathrm{symfalse}& \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$```

Display the data type of `T`, which is `sym`.

`class(F)`
```ans = 'sym' ```

Next, use `symfalse` to generate a 3-by-2-by-2 array of symbolic logical `symfalse`s.

`F = symfalse(3,2,2)`
```F(:,:,1) =  $\left(\begin{array}{cc}\mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$```
```F(:,:,2) =  $\left(\begin{array}{cc}\mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$```

Alternatively, you can use a size vector to specify the size of the array.

`F = symfalse([3,2,2])`
```F(:,:,1) =  $\left(\begin{array}{cc}\mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$```
```F(:,:,2) =  $\left(\begin{array}{cc}\mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$```

Create a truth table for the `and` operation applied to the two symbolic logical constants, `symtrue` and `symfalse`.

`A = [symtrue symfalse]`
`A = $\left(\begin{array}{cc}\mathrm{symtrue}& \mathrm{symfalse}\end{array}\right)$`
`B = [symtrue; symfalse]`
```B =  $\left(\begin{array}{c}\mathrm{symtrue}\\ \mathrm{symfalse}\end{array}\right)$```
`TF = and(A,B)`
```TF =  $\left(\begin{array}{cc}\mathrm{symtrue}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$```

Combine symbolic logical constants with logical operators `and`, `not`, `or`, and `xor` (or their shortcuts).

`TF = xor(symtrue,or(symfalse,symfalse))`
`TF = $\mathrm{symtrue}$`
`TF = symtrue & ~(symfalse)`
`TF = $\mathrm{symtrue}$`

Convert the symbolic logical constant `symfalse` to a logical value.

`T1 = logical(symfalse)`
```T1 = logical 0 ```

Convert the symbolic logical constant `symfalse` to numeric values in double precision and variable precision.

`T2 = double(symfalse)`
```T2 = 0 ```
`T3 = vpa(symfalse)`
`T3 = $0.0$`

Show the data types of `T1`, `T2`, and `T3`.

`whos`
``` Name Size Bytes Class Attributes T1 1x1 1 logical T2 1x1 8 double T3 1x1 8 sym ```

## Input Arguments

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

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

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

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

• 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. For example, `symfalse([2 2 1 1])` returns a 2-by-2 array and `symfalse([2 2 1 2 1])` returns a 2-by-2-by-1-by-2 array.

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

• 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. For example, `symfalse([2,2,1,1])` returns a 2-by-2 array and `symfalse([2,2,1,2,1])` returns a 2-by-2-by-1-by-2 array.

## Output Arguments

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Symbolic logical constant for false condition, returned as a scalar, vector, matrix, or N-D array.

Data Types: `sym`

## Tips

• The command `sym(false)` returns a symbolic number `0`, and `sym(symfalse)` returns `symfalse`.

• When you combine two arrays of symbolic logical constants with logical operations using `and`, `or`, or `xor` function, the arrays must either be the same size or have sizes that are compatible. For more information on the required input sizes for basic array operations, see Compatible Array Sizes for Basic Operations.

## Version History

Introduced in R2020a