Recall the calculated values for each region of the Venn diagram from the previous solution.

Mathematics

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Step-by-step solution

2 steps
  1. Recall the calculated values for each region of the Venn diagram from the previous solution.

    Let C be Cocacola, F be Fanta, and S be Sprite.

    • Students taking all three drinks (C ∩\cap F ∩\cap S): 7
    • Students taking Cocacola and Fanta only (C ∩\cap F only): 9
    • Students taking Cocacola and Sprite only (C ∩\cap S only): 5
    • Students taking Fanta and Sprite only (F ∩\cap S only): 8
    • Students taking Cocacola only (C only): m+3m+3
    • Students taking Fanta only (F only): 12−2m12-2m
    • Students taking Sprite only (S only): mm
    • Students taking none of the drinks: 6
  2. Present the information in a Venn diagram format.

    A Venn diagram consists of a rectangle representing the universal set and overlapping circles for each set (C, F, S). The numbers calculated above are placed in the corresponding regions.

    Here is the breakdown of the regions for the Venn diagram:

    • The central region where all three circles C, F, and S overlap contains: 7\mathbf{7}
    • The region where C and F overlap, but not S, contains: 9\mathbf{9}
    • The region where C and S overlap, but not F, contains: 5\mathbf{5}
    • The region where F and S overlap, but not C, contains: 8\mathbf{8}
    • The region for C only (not overlapping with F or S) contains: m+3\mathbf{m+3}
    • The region for F only (not overlapping with C or S) contains: 12−2m\mathbf{12-2m}
    • The region for S only (not overlapping with C or F) contains: m\mathbf{m}
    • The region outside all three circles (within the universal set) contains: 6\mathbf{6}
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