JavaScript Set Operations

JavaScript Sets store unique values, which makes them ideal for mathematical set operations. Although JavaScript doesn’t provide built-in methods for union or intersection, we can achieve them using spread operators, loops, or helper functions.

1. Union

Combine all unique elements from two sets.

function union(setA, setB) {
  return new Set([...setA, ...setB]);
}

const a = new Set([1, 2, 3]);
const b = new Set([3, 4, 5]);
console.log(union(a, b)); // Set {1, 2, 3, 4, 5}

2. Intersection

Get elements common to both sets.

function intersection(setA, setB) {
  return new Set([...setA].filter(x => setB.has(x)));
}

console.log(intersection(a, b)); // Set {3}

3. Difference

Elements in the first set but not in the second.

function difference(setA, setB) {
  return new Set([...setA].filter(x => !setB.has(x)));
}

console.log(difference(a, b)); // Set {1, 2}

4. Symmetric Difference

Elements in either set, but not in both.

function symmetricDifference(setA, setB) {
  return new Set([...difference(setA, setB), ...difference(setB, setA)]);
}

console.log(symmetricDifference(a, b)); // Set {1, 2, 4, 5}

5. Subset

Check if all elements of one set exist in another.

function isSubsetOf(setA, setB) {
  return [...setA].every(x => setB.has(x));
}

const c = new Set([1, 2]);
console.log(isSubsetOf(c, a)); // true

6. Superset

Check if a set contains all elements of another set.

function isSupersetOf(setA, setB) {
  return [...setB].every(x => setA.has(x));
}

console.log(isSupersetOf(a, c)); // true

7. Disjoint

Check if two sets have no elements in common.

function isDisjointFrom(setA, setB) {
  return ![...setA].some(x => setB.has(x));
}

const d = new Set([6, 7]);
console.log(isDisjointFrom(a, d)); // true
console.log(isDisjointFrom(a, b)); // false

Summary Table

Operation	Description	Example
union	Combine all unique elements	{1,2,3} ∪ {3,4} = {1,2,3,4}
intersection	Common elements	{1,2,3} ∩ {2,3} = {2,3}
difference	In first but not second	{1,2,3} - {2,3} = {1}
symmetricDifference	Elements in either, not both	{1,2} Δ {2,3} = {1,3}
isSubsetOf	All elements of A in B	{1,2} ⊆ {1,2,3} = true
isSupersetOf	All elements of B in A	{1,2,3} ⊇ {1,2} = true
isDisjointFrom	No common elements	{1,2} ∩ {3,4} = ∅