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Solving A Logic Problem with A Venn Diagram

Solving A Logic Problem with A Venn Diagram. Created by E.G. Gascon Problem Section 7.2 #41. The problem . State the Problem in Set Notation. n(T) = 22 n(G) = 25 n(S) = 39 n(T G) = 9 n(G S) = 20 n(T’ G’S’) = 4 n(T GS) = 6.

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Solving A Logic Problem with A Venn Diagram

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  1. Solving A Logic Problem with A Venn Diagram Created by E.G. Gascon Problem Section 7.2 #41

  2. The problem

  3. State the Problem in Set Notation n(T) = 22 n(G) = 25 n(S) = 39 n(TG) = 9 n(GS) = 20 n(T’G’S’) = 4 n(TGS) = 6 I switched the last two because the 6 is the intersections of all the circles in the Venn Diagram.

  4. Building the Venn Diagram from the inside out. Start in the inner most intersection of the diagram, where the three circles all intersect. n(TGS) = 6

  5. Label the area that has NO items n(T’G’S’) = 4

  6. Build out from the center. Next enter the number for the areas where only two circles overlap. What is left, will be placed in the next areas. Part of the intersection of T and G is already = 6 n(TG) = 9 But, … Part of the intersection of G and S is already = 6 n(GS) = 20 But, … x Notice that n(TS) does not have a value. Let it be x.

  7. Continue to work up the list All of S = 39, but there are already 6 + 14 + x object in the set S. Therefore, what is exclusively S is 39 – 6 – 14 - x n(S) = 39

  8. Continue to work up the list All of S = 25, but there are already 6 + 14 + 3 object in the set G. Therefore, what is exclusively G is 25 – 6 – 14 - 3 n(G) = 25

  9. Continue to work up the list All of T = 22, but there are already 6 + 3 + x object in the set T. Therefore, what is exclusively T is 22 – 6 – 3 – x n(T) = 22

  10. Create an equation from the information: Add all the components of the sample space: You are now ready to answer the questions.

  11. a) Tall and Smooth = 11 + 6 = 17 Look at the circle that represents the Tall and the circle that represents the Smooth. Now consider where they overlap.

  12. b.) Tall and NOT (smooth nor Green) = 2 Look at the circle that represent Tall, now take away the whatever is smooth or green in the circle.

  13. c) Not Tall but had peas that were smooth and green = 14 Look outside of the circle that represents Tall. Then consider only the area of overlap between Smooth and Green.

  14. Questions????? If after viewing this slide show, questions still linger on how to solve a problem like this please contact me.

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