Question 1168388: A cat has thirteen kittens. Eight of the kittens have white hair, six of the kittens have spots, and eight of the kittens have long tails. All of the kittens have at least one of these traits. One kitten is white with spots and a long tail. Three of the kittens are white with spots. Two kittens have spots and long tails. One kitten has white hair but does not have spots or a long tail.
A. Draw a Venn diagram for this problem.
B. How many kittens are white with long tails, but don't have spots?
Thank you
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step by step to create the Venn diagram and answer the questions.
**A. Venn Diagram**
1. **Draw the Circles:** Draw three overlapping circles. Label them:
* W: White hair
* S: Spots
* T: Long tails
2. **Total Kittens:** The total number of kittens is 13.
3. **Fill in the Intersections:**
* **W ∩ S ∩ T:** One kitten is white with spots and a long tail. Write "1" in the region where all three circles overlap.
* **W ∩ S:** Three kittens are white with spots. Since one of these has a long tail, there are 3 - 1 = 2 kittens that are white with spots but don't have long tails. Write "2" in the region where W and S overlap but not T.
* **S ∩ T:** Two kittens have spots and long tails. Since one of these has white hair, there are 2 - 1 = 1 kitten that has spots and a long tail but not white hair. Write "1" in the region where S and T overlap but not W.
* **W only:** One kitten has white hair but does not have spots or a long tail. Write "1" in the region of circle W that is not in S or T.
4. **Calculate Remaining Values:**
* **W:** Eight kittens have white hair. We have 1 + 2 + 1 = 4 in circle W so far. There are 8-4=4 kittens that are white with long tails but don't have spots. Write "4" in the region of W and T overlap but not S.
* **S:** Six kittens have spots. We have 2 + 1 + 1 = 4 in circle S so far. There are 6 - 4 = 2 kittens that have spots but don't have white hair or long tails. Write "2" in the region of S that is not in W or T.
* **T:** Eight kittens have long tails. We have 1 + 1 + 4 = 6 in circle T so far. There are 8 - 6 = 2 kittens that have long tails but don't have white hair or spots. Write "2" in the region of T that is not in W or S.
5. **Check Total Kittens:**
* 1 (W only) + 2 (S only) + 2 (T only) + 2 (W ∩ S) + 1 (S ∩ T) + 4 (W ∩ T) + 1 (W ∩ S ∩ T) = 13. This matches the total number of kittens.
**Venn Diagram:**
```
W (8)
/ \
1 4
/ \ / \
2---1---1
\ / \ /
2 2
\ /
S (6)
T (8)
```
**B. How many kittens are white with long tails, but don't have spots?**
* From the Venn diagram, the number of kittens in the region where W and T overlap but not S is 4.
**Answer:**
A. The Venn diagram is shown above.
B. 4 kittens are white with long tails, but don't have spots.
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