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Solving Problems Using Venn Diagram

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Solving Problems Using Venn Diagram

  1. 1. Grade 7 – Mathematics Quarter I SOLVING PROBLEMS USING VENN DIAGRAM
  2. 2. •describe the set notation given by the shaded region in the Venn Diagram; and •solve problems using Venn Diagram.
  3. 3. Describe the set notation given by the shaded region. A AA ∩ B A ∪ B A B A B
  4. 4. Describe the set notation given by the shaded region. A B A - B (B ∪ C) A CB A CB A ∪ B ∪ C A ∩ B’
  5. 5. Describe the set notation given by the shaded region. (A ∩ B)’ (A ∪ B)’(B ∪ C) ∩ A’ A CB AA B A B
  6. 6. INTERSECTION SOLVING PROBLEMS USING VENN DIAGRAM UNION DIFFERENCE COMPLEMENT “and” “or” “neither-nor” “but not” “all three” “neither” “only” “but not”
  7. 7. Let’s try! 1. apple and banana 2. apple or banana 3. apple only 4. apple A – apple B – banana ∩A B ∪A B −A B A n(A ∩ B) n(A ∪ B) n(A − B) n(A)
  8. 8. 5. apple and banana but not orange 6. neither of the three A – apple B – banana O-orange ∩A B A∪B∪O n(A ∩ B) − O n(A∪B∪O)’ − O n(A ∩ B) ∩ O’ ′
  9. 9. 7. all three 8. banana or orange but not apple A – apple B – banana O-orange B n(B ∪ O) ∩ A’ ∩ n(A ∩ B ∩ O) O A∪ − n(B ∪ O) - A
  10. 10. Forty people are asked about the social media accounts that they have. Let F = {people who have Facebook accounts} T = {people who have Twitter accounts} I = {people who have Instagram accounts} How many people have: 1. Facebook accounts? U F 8 6 TI 3 5 7 4 2 n (F) = 8 + 7 + 5 + 2 n (F) = 22 2. Facebook and Twitter accounts? n (F ∩ T) = 7 + 2 n (F ∩ T) = 9 U = 40 people
  11. 11. Forty people are asked about the social media accounts that they have. How many people have: 3. Facebook or Instagram accounts? U F 8 6 TI 3 5 7 4 2 n (F ∪ I) = 8 + 7 + 5 + 2 + 4 + 3 n (F ∪ I) = 29 4. Twitter and Instagram accounts? n (T ∩ I) = 2 + 4 n (T ∩ I) = 6 5. Facebook or Twitter accounts? n (F ∪ T) = 8 + 7 + 5 + 2 + 4 + 6 n (F ∪ T) = 32
  12. 12. Forty people are asked about the social media accounts that they have. How many people have: 6. Facebook accounts only U F 8 6 TI 3 5 7 4 2 n (F – T – I) = 8 7. Twitter and Instagram but not Facebook accounts? n (T ∩ I) - F = 4 8. Facebook or Twitter but not Instagram accounts? n (F ∪ T) – I = 8 + 7 + 6 n (F ∪ T) – I = 21
  13. 13. Forty people are asked about the social media accounts that they have. Let F = {people who have Facebook accounts} T = {people who have Twitter accounts} I = {people who have Instagram accounts} How many people have: 9. all three? U F 8 6 TI 3 5 7 4 2 n (F ∩ T ∩ I) = 2 10. neither one of three? n (F ∪ T ∪ I)’ = 5 U = 40 people n (F ∪ T ∪ I) = 8 + 7 + 5 + 2 + 4 + 3 + 6 = 35 5
  14. 14. A teacher announces that out of 30 students in class, 16 passed both the Math and Science tests, and 24 passed the Science test. U Math Science 16 8 1. How many passed the Math test only? 6 2. How many passed the Science test only? 3. How many students did not pass either Math or Science test? n (M – S) = 0 n (S – M) = 8 n (M ∪ S)’ = 6

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