(i) To represent this information in a Venn Diagram, you would start by drawing three overlapping circles, each representing one of the food types (Pizza, Burgers, Sandwiches).

- In the intersection of all three circles (where they all overlap), you would write '3', as this represents the students who like all three types of food.

- In the intersection of the Pizza and Burgers circles (but not the Sandwiches circle), you would write '9'. This is because 12 students like both Pizza and Burgers, but we've already accounted for 3 of those students in the intersection of all three circles.

- In the intersection of the Burgers and Sandwiches circles (but not the Pizza circle), you would write '5'. This is because 8 students like both Burgers and Sandwiches, but we've already accounted for 3 of those students in the intersection of all three circles.

- In the intersection of the Pizza and Sandwiches circles (but not the Burgers circle), you would write '3'. This is because 6 students like both Pizza and Sandwiches, but we've already accounted for 3 of those students in the intersection of all three circles.

(ii) If the same number of students eat burgers as those who eat pizzas, then the total number of students who like burgers would be the sum of the numbers in the Burgers circle. This would be 3 (students who like all three) + 9 (students who like Pizza and Burgers but not Sandwiches) + 5 (students who like Burgers and Sandwiches but not Pizza) = 17 students.

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(i) To represent this information in a Venn Diagram, you would start by drawing three overlapping circles, each representing one of the food types (Pizza, Burgers, Sandwiches).

- In the intersection of all three circles (where they all overlap), you would write '3', as this represents the students who like all three types of food.

- In the intersection of the Pizza and Burgers circles (but not the Sandwiches circle), you would write '9'. This is because 12 students like both Pizza and Burgers, but we've already accounted for 3 of those students in the intersection of all three circles.

- In the intersection of the Burgers and Sandwiches circles (but not the Pizza circle), you would write '5'. This is because 8 students like both Burgers and Sandwiches, but we've already accounted for 3 of those students in the intersection of all three circles.

- In the intersection of the Pizza and Sandwiches circles (but not the Burgers circle), you would write '3'. This is because 6 students like both Pizza and Sandwiches, but we've already accounted for 3 of those students in the intersection of all three circles.

(ii) If the same number of students eat burgers as those who eat pizzas, then the total number of students who like burgers would be the sum of the numbers in the Burgers circle. This would be 3 (students who like all three) + 9 (students who like Pizza and Burgers but not Sandwiches) + 5 (students who like Burgers and Sandwiches but not Pizza) = 17 students.

Knowee AI · Accepted Answer

(i) To represent this information in a Venn Diagram, you would start by drawing three overlapping circles, each representing one of the food types (Pizza, Burgers, Sandwiches).

- In the intersection of all three circles (where they all overlap), you would write '3', as this represents the students who like all three types of food.

- In the intersection of the Pizza and Burgers circles (but not the Sandwiches circle), you would write '9'. This is because 12 students like both Pizza and Burgers, but we've already accounted for 3 of those students in the intersection of all three circles.

- In the intersection of the Burgers and Sandwiches circles (but not the Pizza circle), you would write '5'. This is because 8 students like both Burgers and Sandwiches, but we've already accounted for 3 of those students in the intersection of all three circles.

- In the intersection of the Pizza and Sandwiches circles (but not the Burgers circle), you would write '3'. This is because 6 students like both Pizza and Sandwiches, but we've already accounted for 3 of those students in the intersection of all three circles.

(ii) If the same number of students eat burgers as those who eat pizzas, then the total number of students who like burgers would be the sum of the numbers in the Burgers circle. This would be 3 (students who like all three) + 9 (students who like Pizza and Burgers but not Sandwiches) + 5 (students who like Burgers and Sandwiches but not Pizza) = 17 students.

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