xor

Logical XOR for symbolic expressions

Syntax

xor(A,B)

Description

xor(A,B) represents the logical exclusive disjunction. xor(A,B) is true when either A or B is true. If both A and B are true or false, xor(A,B) is false.

Examples

Set and Evaluate Condition

Combine two symbolic inequalities into a logical expression using xor.

syms x
range = xor(x > -10, x < 10);

Replace variable x with 11 and 0. If you replace x with 11, then inequality x > -10 is valid and x < 10 is invalid. If you replace x with 0, both inequalities are valid. Note that subs only substitutes the numeric values into the inequalities. It does not evaluate the inequalities to logical 1 or 0.

x1 = subs(range,x,11)
x2 = subs(range,x,0)

x1 =
-10 < 11 xor 11 < 10
 
x2 =
-10 < 0 xor 0 < 10

To evaluate these inequalities to logical 1 or 0, use isAlways. If only one inequality is valid, the expression with xor evaluates to logical 1. If both inequalities are valid, the expression with xor evaluates to logical 0.

isAlways(x1)
isAlways(x2)

ans =
  logical
     1

ans =
  logical
     0

Note that simplify does not simplify these logical expressions to logical 1 or 0. Instead, simplify returns symbolic constants symtrue or symfalse.

s1 = simplify(x1)
s2 = simplify(x2)

s1 =
symtrue
 
s2 =
symfalse

Convert symbolic symtrue or symfalse to logical values using logical.

logical(s1)
logical(s2)

ans =
  logical
     1

ans =
  logical
     0

Input Arguments

A, B — Operands

symbolic equations | symbolic inequalities | symbolic expressions | symbolic arrays

Operands, specified as symbolic equations, inequalities, expressions, or arrays. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

Tips

• If you call simplify for a logical expression containing symbolic subexpressions, you can get the symbolic constants symtrue and symfalse. These two constants are not the same as logical 1 (true) and logical 0 (false). To convert symbolic symtrue and symfalse to logical values, use logical.

• assume and assumeAlso do not accept assumptions that contain xor.

Version History

Introduced in R2012a

R2016b: Implicit expansion change affects arguments for operators

Starting in R2016b with the addition of implicit expansion, some combinations of arguments for basic operations that previously returned errors now produce results. For example, you previously could not add a row and a column vector, but those operands are now valid for addition. In other words, an expression like [1 2] + [1; 2] previously returned a size mismatch error, but now it executes.

If your code uses element-wise operators and relies on the errors that MATLAB^® previously returned for mismatched sizes, particularly within a try/catch block, then your code might no longer catch those errors.

For more information on the required input sizes for basic array operations, see Compatible Array Sizes for Basic Operations.