Question

question 2 of 7
in the venn diagram, circles s, c, and p represent farms raising sheep, cows, and pigs, respectively. how many of the 47 farms represented in the diagram do not raise cows?
12, 13, 10, 2, 1, 4, 5 (in the venn diagram)
options: 15, 17, 18, 19

Explanation:

Step1: Identify regions not in C

We need to find the number of farms that do not raise cows, so we consider the regions outside circle C (which represents cows). These regions are the parts of circles S (sheep) and P (pigs) that don't overlap with C.

Step2: Sum the relevant regions

The regions not in C are: the part of S only (12), the part of S and P only (2), the part of P only (5). Wait, no, wait. Wait, the Venn diagram has S, C, P. Let's list the regions not in C:

• Only S: 12
• S and P only (the region where S and P overlap but not C): 2
• Only P: 5
• Wait, is there any other? Wait, no, the regions not in C are:

12 (only S) + 2 (S and P only) + 5 (only P) + wait, no, wait, maybe I missed? Wait, no, let's check the Venn diagram again. The circles are S, C, P. The regions:

• Only S: 12
• S and C only: 13
• C only: 10
• S and P only: 2
• S, C, P: 1
• C and P only: 4
• Only P: 5

So the regions not in C are: only S (12), S and P only (2), only P (5), and is there any other? Wait, no, because C is the cow circle. So the areas not in C are:

12 (only S) + 2 (S ∩ P only) + 5 (only P) + wait, no, wait, maybe I made a mistake. Wait, the total farms not raising cows would be the sum of all regions that do not include C. So:

Only S: 12

S and P only (the region where S and P overlap but not C): 2

Only P: 5

Wait, but also, is there a region that's only S and P? Wait, the Venn diagram has:

• S only: 12

• S ∩ C only: 13

• C only: 10

• S ∩ P only: 2

• S ∩ C ∩ P: 1

• C ∩ P only: 4

• P only: 5

So the regions not in C are:

Only S (12) + S ∩ P only (2) + Only P (5) + wait, no, that's 12 + 2 + 5 = 19? Wait, no, wait, 12 + 2 + 5 = 19? Wait, but let's check again. Wait, 12 (only S) + 2 (S and P only) + 5 (only P) = 12 + 2 + 5 = 19? Wait, but let's add them: 12 + 2 is 14, 14 + 5 is 19. Wait, but let's verify with another approach. Alternatively, we can calculate total farms minus farms that raise cows.

Total farms: 47.

Farms that raise cows: regions in C. Let's calculate farms that raise cows:

Only C: 10

S ∩ C only: 13

C ∩ P only: 4

S ∩ C ∩ P: 1

So sum of regions in C: 10 + 13 + 4 + 1 = 28

Then farms not raising cows: total (47) - farms raising cows (28) = 19. Ah, that's a better approach. Let's do that.

Step3: Calculate total in C

Farms raising cows (in C) are:

• Only C: 10

• S and C only: 13

• C and P only: 4

• S, C, P: 1

Sum these: 10 + 13 + 4 + 1 = 28

Step4: Subtract from total

Total farms: 47

Farms not raising cows: 47 - 28 = 19

Answer:

19