A set is a collection of any type of comparable data. Data in a set can occur only once.

Example;

```
{..., -3, -1, 1, 3, ...} is a set of odd numbers
```

## Basic Set Implementations

**new Set()** - create a new set

**Set.prototype.has()** - returns true if element is present in Set object

**Set.prototype.add()** - adds a new item to set object

**Set.prototype.delete()** - removes specified item from set object

**1.Union Algorithm**

This is a set algorithm that compares two sets and returns a third set that contains all of the unique items in both sets.

```
function union(setA, setB) {
let result = new Set(setA); // new set containing items in setA
for (let elem of setB) {
// add items from setB to the new set
// an element can't be added twice
result.add(elem);
}
return result;
}
let setA = new Set([1, 2, 3]);
let setB = new Set([3, 4, 5]);
console.log(union(setA, setB));
// >> Set { 1, 2, 3, 4, 5 }
```

**2.Intersection Algorithm**

Compares two sets and returns a third set that contains all of the matching members of both sets.

```
function intersection(setA, setB) {
let result = new Set(); // new empty set
for (let elem of setA) {
if (setB.has(elem)){ // if matching elements found
result.add(elem); // add to new set
}
}
return result;
}
let setA = new Set([1, 2, 3]);
let setB = new Set([2, 3, 4]);
console.log(intersection(setA, setB));
// >> Set { 2, 3 }
```

**3.Set Difference Algorithm**

Takes two sets, A and B, and return all the items of A that are not members of B.

```
function setDifference(setA, setB) {
let result = new Set(setA);
for (let item of setB) {
result.delete(item); // delete items in A that exist in B
}
return result;
}
let setA = new Set([2, 3, 4]);
let setB = new Set([3, 4, 5]);
console.log(setDifference(setA, setB));
// >> Set { 2 }
```

**4.Symmetric Difference Algorithm**

Takes two sets and returns a third set that contains all of the members of both sets that are not in the other

```
function symmetricDifference(setA, setB) {
let difference = new Set(setA);
for (let elem of setB) {
if (difference.has(elem)) {
difference.delete(elem); // if item in B exists in A, remove
} else {
difference.add(elem) // else add to new set
}
}
return difference;
}
let setA = new Set([1, 2, 3]);
let setB = new Set([2, 3, 4]);
console.log(symmetricDifference(setA, setB));
// >> Set { 1, 4 }
```

Symmetric Difference can also be described as the set difference of the intersection and union of the input sets

```
function symmetricDifference(setA, setB) {
let intersectionResult = intersection(setA, setB)
let unionResult = union(setA, setB);
return setDifference(unionResult, intersectionResult,)
}
let setA = new Set([1, 2, 3]);
let setB = new Set([2, 3, 4]);
console.log(symmetricDifference(setA, setB));
// >> Set { 1, 4 }
```

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