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Set Theory

Advanced

Discrete Mathematics

Concept

Sets, operations, relations, functions, and cardinality.

Walkthrough

Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Find A ∪ B and A ∩ B.

  1. 1.Recall the definitions: union (A ∪ B) is the set of all elements in A or B (or both); intersection (A ∩ B) is the set of elements in both A and B.
  2. 2.Find A ∪ B: combine all elements from both sets without duplicates: {1, 2, 3, 4, 5, 6}.
  3. 3.Find A ∩ B: identify elements that appear in both A and B: 3 and 4 are in both sets.
  4. 4.So A ∩ B = {3, 4}.
  5. 5.Final answer: A ∪ B = {1, 2, 3, 4, 5, 6} and A ∩ B = {3, 4}.

Answer

A ∪ B = {1, 2, 3, 4, 5, 6}, A ∩ B = {3, 4}

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