Subjects set theory

Farms No Cows 3F7214

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1. **State the problem:** We have a Venn diagram with three sets: S (sheep), C (cows), and P (pigs). The numbers inside represent farms raising those animals. We want to find how many of the 47 farms do **not** raise cows. 2. **Identify the numbers in the Venn diagram:** - Only S: 12 - S and C: 13 - Only C: 10 - S and P: 2 - All three (S, C, P): 1 - C and P: 4 - Only P: 5 3. **Total farms:** The problem states there are 47 farms in total. 4. **Find farms that raise cows:** These are the farms in any region that includes C: - Only C: 10 - S and C: 13 - C and P: 4 - All three: 1 Sum these: $$10 + 13 + 4 + 1 = 28$$ 5. **Find farms that do NOT raise cows:** Subtract farms that raise cows from total farms: $$47 - 28 = 19$$ 6. **Answer:** 19 farms do not raise cows. Therefore, the correct choice is J. 19.