and

Logical AND for symbolic expressions

Syntax

A & B

and(A,B)

Description

A & B represents the logical AND. A & B is true only when both A and B are true.

and(A,B) is equivalent to A & B.

Examples

Construct and Set Assumptions Using AND

Combine symbolic inequalities into one condition by using &.

syms x y
cond = x>=0 & y>=0;

Set the assumptions represented by the condition using assume.

assume(cond)

Verify that the assumptions are set.

assumptions

ans =
[ 0 <= x, 0 <= y]

Evaluate Inequalities or Conditions

Define a range for a variable by combining two inequalities into a logical condition using &.

syms x
range = 0 < x & x < 1;

Return the condition at 1/2 and 10 by substituting for x using subs. The subs function does not evaluate the conditions automatically.

x1 = subs(range,x,1/2)
x2 = subs(range,x,10)

x1 =
0 < 1/2 & 1/2 < 1
x2 =
0 < 10 & 10 < 1

Evaluate the inequalities to logical 1 or 0 by using isAlways.

isAlways(x1)
isAlways(x2)

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.

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.