# # Set operations

## # Elementary set operations

It's possible to perform elementary set operations with Matlab. Let's assume we have given two vectors or arrays

```
A = randi([0 10],1,5);
B = randi([-1 9], 1,5);
```

and we want to find all elements which are in `A`

and in `B`

. For this we can use

```
C = intersect(A,B);
```

`C`

will include all numbers which are part of `A`

and part of `B`

.
If we also want to find the position of these elements we call

```
[C,pos] = intersect(A,B);
```

`pos`

is the position of these elements such that `C == A(pos)`

.

Another basic operation is the union of two sets

```
D = union(A,B);
```

Herby contains `D`

all elements of `A`

and `B`

.

Note that `A`

and `B`

are hereby treated as sets which means that it does not matter how often an element is part of `A`

or `B`

. To clarify this one can check
`D == union(D,C)`

.

If we want to obtain the data that is in 'A' but not in 'B' we can use the following function

```
E = setdiff(A,B);
```

We want to note again that this are sets such that following statement holds `D == union(E,B)`

.

Suppose we want to check if

```
x = randi([-10 10],1,1);
```

is an element of either `A`

or `B`

we can execute the command

```
a = ismember(A,x);
b = ismember(B,x);
```

If `a==1`

then `x`

is element of `A`

and `x`

is no element is `a==0`

. The same goes for `B`

. If `a==1 && b==1`

`x`

is also an element of `C`

. If `a == 1 || b == 1`

`x`

is element of `D`

and if `a == 1 || b == 0`

it's also element of `E`

.

#### # Syntax

- C = union(A,B);
- C = intersect(A,B);
- C = setdiff(A,B);
- a = ismember(A,x);

#### # Parameters

Parameter | Details |
---|---|

A,B | sets, possibly matrices or vectors |

x | possible element of a set |