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Simplifying Set Operations with Venn Diagrams

This document presents a comprehensive guide to simplifying set operations using Venn diagrams. It demonstrates the step-by-step process of applying set algebra to expressions such as (A ∪ B) ∩ (A ∪ B′) and others. By breaking down complex expressions, we aim to make understanding intersections and unions more accessible for students and educators alike. The use of Venn diagrams visually illustrates relationships between sets, providing clarity on multiple algebraic statements while facilitating easier learning outcomes.

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Simplifying Set Operations with Venn Diagrams

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  1. SIMPLIFY using a Venn Diagram Pamela Leutwyler

  2. A B 1 2 3 4

  3. A B 1 2 3 4 A  B

  4. A B 1 2 3 4 A - B

  5. A B 1 2 3 4 B - A

  6. A B 1 2 3 4

  7. A B 1 2 3 4 simplify: ( A  B )  ( A  B  )

  8. A B 1 2 3 4 simplify: ( A  B )  ( A  B  ) 1, 2, 3

  9. A B 1 2 3 4 simplify: ( A  B )  ( A B  ) 1, 2, 3  1, 2

  10. A B 1 2 3 4 simplify: ( A  B )  ( A  B  ) 1, 2, 3  ( 1, 2  2, 4 )

  11. A B 1 2 3 4 simplify: ( A  B )  ( A  B  ) 1, 2, 3  ( 1, 2  2, 4 )

  12. A B 1 2 3 4 simplify: ( A  B )  ( A  B  ) 1, 2, 3  ( 1, 2  2, 4 ) 1, 2, 3  ( 1, 2, 4 )

  13. A B 1 2 3 4 simplify: ( A  B )  ( A  B  ) 1, 2, 3  ( 1, 2  2, 4 ) 1, 2, 3  ( 1, 2, 4 )

  14. A B 1 2 3 4 simplify: ( A  B )  ( A  B  ) = A 1, 2, 3  ( 1, 2  2, 4 ) 1, 2, 3  ( 1, 2, 4 ) 1, 2

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