Question

Carl Cornfield represented the acres he planted with a Venn diagram. A = {corn}; B = {wheat}; U = {all grain}. Answer the following questions: How many acres were planted in just corn? How many acres were planted in just wheat? What is the intersection of corn and wheat? What is the union of corn and wheat?

Answer 1

Answers:

• Just corn = 10 acres
• Just wheat = 7 acres
• Intersection of corn and wheat = 4 acres
• Union of corn and wheat = 21 acres

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Explanation:

The number 10 inside circle A, but outside circle B, represents the number of acres dedicated to corn only (no wheat).

The number 7 inside circle B, but outside circle A, represents the number of acres dedicated to wheat only (no corn)

The number 4 in the overlapping region of both circles represents the number of acres for both corn and wheat at the same time.

The union of two sets is simply combining the two sets together to form one bigger set. If an element is in A union B, then it is either in A or B, or both. We add the values in the circles to get 10+7+4 = 17+4 = 21 to represent 21 acres for corn only, for wheat only, or for both.

Note: There are no values outside the circles, so none of the land is for any other purpose other than corn or wheat.

Check out the diagram below for a visual summary.