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# le

Define less than or equal to relation

In previous releases, `le` in some cases evaluated inequalities involving only symbolic numbers and returned logical `1` or `0`. To obtain the same results as in previous releases, wrap inequalities in `isAlways`. For example, use `isAlways(A <= B)`.

## Syntax

`A <= Ble(A,B)`

## Description

`A <= B` creates a less than or equal to relation.

`le(A,B)` is equivalent to `A <= B`.

## Input Arguments

 `A` Number (integer, rational, floating-point, complex, or symbolic), symbolic variable or expression, or array of numbers, symbolic variables or expressions. `B` Number (integer, rational, floating-point, complex, or symbolic), symbolic variable or expression, or array of numbers, symbolic variables or expressions.

## Examples

Use `assume` and the relational operator `<=` to set the assumption that `x` is less than or equal to 3:

```syms x assume(x <= 3)```

Solve this equation. The solver takes into account the assumption on variable `x`, and therefore returns these three solutions.

`solve((x - 1)*(x - 2)*(x - 3)*(x - 4) == 0, x)`
```ans = 1 2 3```

Use the relational operator `<=` to set this condition on variable `x`:

```syms x cond = (abs(sin(x)) <= 1/2);```
```for i = 0:sym(pi/12):sym(pi) if subs(cond, x, i) disp(i) end end```

Use the `for` loop with step π/24 to find angles from 0 to π that satisfy that condition:

```0 pi/12 pi/6 (5*pi)/6 (11*pi)/12 pi```

## Alternatives

You can also define this relation by combining an equation and a less than relation. Thus, `A <= B` is equivalent to `(A < B) | (A == B)`.

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### Tips

• Calling `<=` or `le` for non-symbolic `A` and `B` invokes the MATLAB® `le` function. This function returns a logical array with elements set to logical ```1 (true)``` where `A` is less than or equal to `B`; otherwise, it returns logical ```0 (false)```.

• If both `A` and `B` are arrays, then these arrays must have the same dimensions. ```A <= B``` returns an array of relations ```A(i,j,...) <= B(i,j,...)```

• If one input is scalar and the other an array, then the scalar input is expanded into an array of the same dimensions as the other array. In other words, if `A` is a variable (for example, `x`), and `B` is an m-by-n matrix, then `A` is expanded into m-by-n matrix of elements, each set to `x`.

• The field of complex numbers is not an ordered field. MATLAB projects complex numbers in relations to a real axis. For example, ```x <= i``` becomes `x <= 0`, and ```x <= 3 + 2*i``` becomes `x <= 3`.