What is a Union in Set Theory? A 23-Year-Old Student Guide

Learn what a union means in set theory, how to compute A ∪ B with step-by-step examples, and see where unions appear in everyday problems. Helpful for CS.

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What is a union?

In math, a union combines elements from two or more sets. For sets A and B, the union A ∪ B contains all elements that are in A or in B (or in both).

  1. Identify the sets: Decide which sets you are uniting (A, B, etc.).
  2. Write the union: Use the symbol ∪, and form A ∪ B.
  3. Compute with an example: If A = {1,2,3} and B = {3,4,5}, then A ∪ B = {1,2,3,4,5}.
  4. Key properties
    • Commutative: A ∪ B = B ∪ A
    • Associative: (A ∪ B) ∪ C = A ∪ (B ∪ C)
    • Identity: A ∪ empty set = A
  5. Notation and further ideas: The empty set ∅ is the identity element; you can build unions of many sets.
  6. Practice: Try A = {1,2} and B = {2,3,4}; A ∪ B = {1,2,3,4}.

Note: If you meant labor unions, see the short note below.

Other meaning: labor union

A labor union is a group formed by workers to protect and negotiate for wages, benefits, and working conditions with employers. They focus on workplace rights and collective bargaining.

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