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Doha

Set Notations And Venn Diagrams

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Published in: Mathematics | SAT | Statistics
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A detailed study of Sets and Venn Diagrams

Saima J / Doha

4 years of teaching experience

Qualification: Master of Science in Materials Engineering

Teaches: Chemical, Maths, Chemistry, Physics, Science, Advanced Maths, Science Projects

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  1. Set Notation and Venn Diagrams Understanding Sets, Operations, and Representations
  2. What is a Set? • A set is a collection of elements. Elements can be numbers, letters, coordinates, etc. • Set Notation: Use curly brackets o. • Example: {1, 2, 3, 6} is the set of factors of 6. • Rule-Based Sets: {x I < 30} = Colon (:) or bar (l) is read as 'such that'.
  3. The Universal Set • Represented by calligraphic E (E). • Defj_njtjgmThe set of everything under consideration. • Example: If interested in factors of 24, E {1 2, 3, 4, 6, 8, 12, 24}. • Alternative notations: U, S, (xi).
  4. Set Operations • Intersection (A n B): Elements in both A and B. Example: A = {1, 2, 3}, B = {2, 3, 4} —A n B = {2, 3}. • Union (A u B): Elements in A, B, or both. Example: A = {1, 2}, B = {3, 4} —A U B = {1, 2, 3, 4}. • Complement (A'): Elements in E but not in A. Example: E = {1, 2, 3, 4}, A = {1, 3} A' = {2, 4}. • Question: IfA= {1, 3}, B = {2, 3, 4}, what isA n B?
  5. Subsets and Empty Sets • Subset (A C B): All elements of A are in B. Example: A {1, 2}, B {1, 2, 3} —A c B. • Not a Subset (A C B): At least one element of Ais not in B. • Empty Set (Ø): A set with no elements. • Question: If A = {4}, B {1, 2, 3}, is A C B true?
  6. What is a Venn Diagram? • Definition: A way to visually represent sets and their relationships. • Components: - Rectangle: Universal set (E). - Circles: Individual sets. - Overlaps: Intersections. Example: A n B is the overlapping area of A and B. Question: If A = {2, 4}, B = {4, 6}, what is A u B?
  7. What do the different regions mean on a Venn diagram? • (A u B) is represented by the region where the A and B circles overlap • (A nB)is represented by the regions that are in A or B or both •A OR a OR BOTH' A' 'COMPLEMENT) • NOT A • An B (INTERSECTION) •A ANO
  8. Worked Example •Two sets A and B are shown in a Venn diagram. • (a) Write down n(A): A {2, 6, 12, 14, 28} Ans: n(A) 5. • (b) Complete: {14, 28} Arts: An B. 42 8 7 44 24 6 28 2 5 35
  9. Worked Example(Contd.) (c) Find Au B: Ans:Au B = {2, 6, 7, 12, 14, 21, 28, 35}. • (d) Jamie states A' n B' = Ø. Explain why this is incorrect. Ans: There are elements not in A or B, so Conclusion: Jamie's statement is incorrect.
  10. o Key Takeaways • Set Definitions and Notation: Curly brackets {}, colon (:), and bar (I). • Operations: Intersection, union, complement. • Universal Set and Subsets: Relationships and representations. • Venn Diagrams: Visualizing sets and overlaps. • Question: Which concept did you find most challenging and why?

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