and, &

Find logical AND

Syntax

A & B

and(A,B)

Description

A & B performs a logical AND of inputs A and B and returns an array or a table containing elements set to either logical 1 (true) or logical 0 (false). An element of the output is set to logical 1 (true) if both A and B contain a nonzero element at that same location. Otherwise, the element is set to 0.

For bit-wise logical AND operations, see bitand.

and(A,B) is an alternate way to execute A & B, but is rarely used. It enables operator overloading for classes.

Examples

Locate Nonzero Values

Find the logical AND of two matrices. The result contains logical 1 (true) only where both matrices contain nonzero values.

A = [5 7 0; 0 2 9; 5 0 0]

A = 3×3

     5     7     0
     0     2     9
     5     0     0

B = [6 6 0; 1 3 5; -1 0 0]

B = 3×3

     6     6     0
     1     3     5
    -1     0     0

A & B

ans = 3×3 logical array

   1   1   0
   0   1   1
   1   0   0

Truth Table for Logical AND

Create a truth table for and.

A = [true false]

A = 1×2 logical array

   1   0

B = [true; false]

B = 2×1 logical array

   1
   0

C = A&B

C = 2×2 logical array

   1   0
   0   0

Logical AND of Tables

Since R2023a

Create two tables and perform a logical AND of them. The row names (if present in both) and variable names must be the same, but do not need to be in the same orders. Rows and variables of the output are in the same orders as the first input.

A = table([0;2],[0;4],VariableNames=["V1","V2"],RowNames=["R1","R2"])

A=2×2 table
          V1    V2
          __    __

    R1    0     0 
    R2    2     4 

B = table([4;2],[3;0],VariableNames=["V2","V1"],RowNames=["R2","R1"])

B=2×2 table
          V2    V1
          __    __

    R2    4     3 
    R1    2     0 

A & B

ans=2×2 table
           V1       V2  
          _____    _____

    R1    false    false
    R2    true     true 

Input Arguments

A, B — Operands

scalars | vectors | matrices | multidimensional arrays | tables | timetables

Operands, specified as scalars, vectors, matrices, multidimensional arrays, tables, or timetables. 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.

Inputs that are tables or timetables must meet the following conditions: (since R2023a)

• If an input is a table or timetable, then all its variables must have data types that support the operation.

• If only one input is a table or timetable, then the other input must be a numeric or logical array.

• If both inputs are tables or timetables, then:

  • Both inputs must have the same size, or one of them must be a one-row table.

  • Both inputs must have variables with the same names. However, the variables in each input can be in a different order.

  • If both inputs are tables and they both have row names, then their row names must be the same. However, the row names in each input can be in a different order.

  • If both inputs are timetables, then their row times must be the same. However, the row times in each input can be in a different order.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | table | timetable

Tips

• You can chain together several logical operations, for example, A & B | C.

• The symbols & and && perform different operations in MATLAB^®. The element-wise AND operator described here is &. The short-circuit AND operator is &&.

• When you use the element-wise & and | operators in the context of an if or while loop expression (and only in that context), they use short-circuiting to evaluate expressions. Otherwise, you must specify && or || to opt-in to short-circuiting behavior. See Short-Circuit AND and Short-Circuit OR for more information.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

The and function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The and function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2023a: Perform operations directly on tables and timetables

The and operator supports operations directly on tables and timetables without indexing to access their variables. All variables must have data types that support the operation. For more information, see Direct Calculations on Tables and Timetables.

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.