Four good friends, who love cats, have each named their cat after one of the other friends. Of the clues that follow, only one is true; the others are false. Which friend owns which cat?

a.Candy’s cat is named either Dody or Alice.
b.Betsy’s cat is named Alice.
c.Either the cat named Candy or the cat named Betsy is owned by Dody.
d.Neither the cat named Betsy nor the cat named Candy belongs to Alice.
e.The cat named Dody does not belong to Candy or Betsy.

To solve this puzzle and determine which friend owns which cat, we need to carefully analyze each clue and determine which one is true. Let's go through each statement one by one:

a. Candy’s cat is named either Dody or Alice.
This clue tells us that Candy's cat is named either Dody or Alice. So, Candy does not own a cat named Candy, as stated. We also have no information about Dody or Alice owning the other cat.

b. Betsy’s cat is named Alice.
According to this clue, Betsy's cat is named Alice.

c. Either the cat named Candy or the cat named Betsy is owned by Dody.
This statement tells us that either Candy's cat or Betsy's cat is owned by Dody. Since Betsy's cat is named Alice (as per clue b), this means Candy's cat must be owned by Dody.

d. Neither the cat named Betsy nor the cat named Candy belongs to Alice.
Based on this clue, we know that Alice does not own either Betsy's cat or Candy's cat. Since Betsy's cat is named Alice (as per clue b), this confirms that Candy's cat must be owned by Dody.

e. The cat named Dody does not belong to Candy or Betsy.
This clue states that Dody's cat is not owned by Candy or Betsy. As we already established, Candy's cat is owned by Dody, so this means Betsy's cat must be named Dody.

Based on all the clues, we can now determine who owns which cat:
- Candy owns Dody's cat.
- Betsy owns Alice.
- Dody owns Candy's cat.
- Alice's owner is unknown.

So the answer to the puzzle is:
- Candy owns Dody's cat.
- Betsy owns Alice.
- Dody owns Candy's cat.
- The owner of the cat named Alice is unknown.