# symfalse

Symbolic logical constant false

## Syntax

``F = symfalse``

## Description

example

````F = symfalse` returns the symbolic logical constant for the false condition.```

## 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 `symfalse`, 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 ```

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 ```

## Output Arguments

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Symbolic logical constant for false condition, returned as a scalar.

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 (MATLAB).