# Union

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**Union** (`∪`

) is a dyadic set function which computes the set union of the two vector arguments.

## Examples

Both arguments of Intersection is usually restricted to vectors. Unlike sets in the mathematical sense, duplicate elements are allowed in both sides, and Union is usually implemented as "left argument unchanged, plus the elements of right argument not in the left argument" `X,(~Y∊X)/Y`

. This preserves the order and multiplicity in both arguments, the left one taking precedence. Both arguments can be nested arrays.

```
'WASH' ∪ 'SHOUT'
WASHOUT
1 2 3 1 2 3 1 2 3∪5 4 3 2 5 4 3 2
1 2 3 1 2 3 1 2 3 5 4 5 4
'THIS' 'THAT' 'THE' 'OTHER'∪'OTHER' 'THAN' 'THIS' 'AND' 'THAT'
┌────┬────┬───┬─────┬────┬───┐
│THIS│THAT│THE│OTHER│THAN│AND│
└────┴────┴───┴─────┴────┴───┘
```

## Extension

Some dialects allow Union to work on major cells:

```
X←4 2⍴'AABBCCCC'
Y←3 2⍴'AADDAA'
X∩Y
AA
BB
CC
CC
DD
```

Works in: Extended Dyalog APL

Others can easily define such a function:

```
X←4 2⍴'AABBCCCC'
Y←3 2⍴'AADDAA'
Intersection←{⍺⌿⍨(≢⍵)≥⍵⍳⍺}
X Intersection Y
AA
BB
CC
CC
DD
```

Works in: Dyalog APL

## External Links

### Documentation