👉 Adds, or the addition of sets, is a fundamental operation in set theory that combines two or more sets into a new set containing all unique elements from each original set. Given sets A, B, and C, the addition of A and B, denoted as A ∪ (B ∩ A) or simply A ∊ {A ∪ B}, results in a set that includes every element from both A and B, with no duplicates. The intersection (B ∩ A) is included only if B and A share common elements; otherwise, it's just A. This operation helps in constructing larger sets from smaller ones while preserving distinctiveness, and it's crucial for various mathematical proofs and constructions, especially in combinatorics and probability theory.
