Draw a Venn diagram to represent the relationships among the

Draw a Venn diagram to represent the relationships among the categories and answer the questions.

The staff at Tiny Little Cherubs (abbreviated TLC) day-care center observed the eating habits of their 64 students during several lunches. They observed that 59 children ate green beans, 56 ate cauliflower, 60 ate broccoli, 55 ate green beans and cauliflower, 54 ate cauliflower and broccoli, 56 ate green beans and broccoli, and 53 ate all three. How many children did not eat any of these three types of vegetables? How many children ate green beans but not cauliflower? How many children did not eat broccoli? How many children ate only cauliflower? How many children ate exactly two of these three vegetables?

*I\'m a little confused about my Venn diagram. What would the universal set be? Students or Vegetables? The sets represent vegetables eaten, so wouldn\'t that be the universal set? The wording of the problem is slightly confusing because it introduces the amount of students first.

*Next, I drew 3 circles that intersect. Set A= Green Beans, Set B= Cauliflower, Set C (intersection bw Set A & Set B)= Green Beans & Cauliflower, Set D (intersection bw Set A & Set G)= Green Beans & Broccoli, Set E (intersection bw all 3 circles)= All 3 (Green Beans, Cauliflower, & Broccoli), Set F ( intersection bw Set B & Set G)= Cauliflower & Broccoli, Set G= Broccoli, and Set H (area outside of the circles)= None of the 3 types (Neither Green Beans, Cauliflower, nor Broccoli). For Set A= 1, Set B= 0, Set C= 2, Set D= 3, Set E= 53, Set F= 1, Set G= 3, and Set H= 1.

Question 1= 1

Question 2= 1

Does that mean just green beans or green beans and broccoli?

Question 3= 2

Does that mean both green beans & cauliflower, if so, then wouldn\'t that be Set C?

Question 4= 0

Question 5= 6

That would be sets C, D, & F right?

*I\'m still unsure if my answers are correct. Could you please help me make sure?

*Also, could you please show a picture of the Venn diagram with the numbers included? I\'m a visual learner so that will help me understand the process a little better.

-Thanks!

Solution