Finite Math - Sizes of Sets

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How to manipulate Venn Diagram to determine sizes of sets

How to algebraically determine sizes of sets:
n(A U B) = n(A) + n(B) – n(A ∩ B)
n(A) + n(A’) = n(U)
n(A ∩ B) + n(A ∩ B’) = n(A)

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  • Finite Math - Sizes of Sets

    1. 1. 1.3Sizes of Sets
    2. 2. Representing Set Sizeson Venn Diagram Let n(U) = 10, n(A) = 7, n(B) = 6, n(A ∩B) = 4. A B Realize n(A U B) = 9, n(A U B)’ = 1.
    3. 3. Representing Set Sizeson Venn Diagram Let n(U) = 10, n(A) = 7, n(B) = 6, n(A ∩B) = 4. A B 4 Realize n(A U B) = 9, n(A U B)’ = 1.
    4. 4. Representing Set Sizeson Venn Diagram Let n(U) = 10, n(A) = 7, n(B) = 6, n(A ∩B) = 4. A B 4 2 Realize n(A U B) = 9, n(A U B)’ = 1.
    5. 5. Representing Set Sizeson Venn Diagram Let n(U) = 10, n(A) = 7, n(B) = 6, n(A ∩B) = 4. A B 3 4 2 Realize n(A U B) = 9, n(A U B)’ = 1.
    6. 6. Representing Set Sizeson Venn Diagram Let n(U) = 10, n(A) = 7, n(B) = 6, n(A ∩B) = 4. A B 3 4 2 1 Realize n(A U B) = 9, n(A U B)’ = 1.
    7. 7. Representing Set Sizeson Venn Diagram Let n(U) = 10, n(A) = 7, n(B) = 6, n(A ∩B) = 4. A B 3 4 2 1 Realize n(A U B) = 9, n(A U B)’ = 1.
    8. 8. Quiz 1.3.1 Let n(U) = 12, n(A) = 6, n(B) = 5, n(A ∩B) = 3. What is n(A U B)’ ? A. 2 B. 3 C. 4
    9. 9. Quiz 1.3.1 Let n(U) = 12, n(A) = 6, n(B) = 5, n(A ∩B) = 3. What is n(A U B)’ ? A. 2 B. 3 C. 4
    10. 10. Quiz 1.3.1 Let n(U) = 12, n(A) = 6, n(B) = 5, n(A ∩B) = 3. What is n(A U B)’ ? A. 2 B. 3 C. 4 Answer: C
    11. 11. Useful Formula Inclusion-exclusion: n(A U B) = n(A) + n(B) – n(A ∩ B) A B Count the middle twice, take it out once
    12. 12. Quiz 1.3.2 Let n(A U B) = 8, n(A) = 4, n(B) = 6; what is n(A ∩ B)? A. 1 B. 2 C. 8
    13. 13. Quiz 1.3.2 Let n(A U B) = 8, n(A) = 4, n(B) = 6; what is n(A ∩ B)? A. 1 B. 2 C. 8 Answer: B
    14. 14. More Useful Formulas n(A) + n(A’) = n(U) [any set and its complement adds up to the universal set] n(A ∩ B) + n(A ∩ B’) = n(A) A B
    15. 15. Quiz 1.3.3 Let A and B be sets in the Universe; n(U) = 10, n(A’) = 6 n(A ∩B) = 2. What is n(A ∩B’)? A. 1 B. 2 C. 3
    16. 16. Quiz 1.3.3 Let A and B be sets in the Universe; n(U) = 10, n(A’) = 6 n(A ∩B) = 2. What is n(A ∩B’)? A. 1 B. 2 C. 3
    17. 17. Quiz 1.3.3 Let A and B be sets in the Universe; n(U) = 10, n(A’) = 6 n(A ∩B) = 2. What is n(A ∩B’)? A. 1 B. 2 C. 3 Answer: B
    18. 18. Summary How to manipulate Venn Diagram to determine sizes of sets How to algebraically determine sizes of sets:  n(A U B) = n(A) + n(B) – n(A ∩ B)  n(A) + n(A’) = n(U)  n(A ∩ B) + n(A ∩ B’) = n(A)
    19. 19.  Features  27 Recorded Lectures  Over 116 practice problems with recorded solutions  Discussion boards/homework help  Visit finitehelp.com to find out more For special offers and additional content...Follow us on twitter @finitehelp Become a fan on Facebook

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