Lalph Rauren was famous for discovering potential models as he walked the streets of New York. One day he spotted four girls who later became top models: Amy, Mary, Kay, and Beth. One was discovered walking through an apartment building, one in a coffee shop, one in a shopping mall, and one in the library. You know the following.
a.If Kay was not discovered in the library, then Amy was discovered in the apartment building.
b.Beth was discovered in the library, unless Mary was discovered in the coffee shop.
c.If Amy was discovered in the apartment building, then Mary was discovered in the shopping mall.
d.If Beth was not discovered in the library, then neither was Kay.
If you have enough information from the statements above, match the girl with the location in which she was discovered and explain your reasoning. If you cannot make the match, explain why.
To solve this problem, we can use logic and deduction to determine the matching of the girls with the locations where they were discovered.
Let's analyze each statement one by one and see what information we can gather from them.
Statement a: "If Kay was not discovered in the library, then Amy was discovered in the apartment building."
From this statement, we know that if Kay was not discovered in the library, then Amy was discovered in the apartment building.
Statement b: "Beth was discovered in the library unless Mary was discovered in the coffee shop."
This statement tells us that if Mary was discovered in the coffee shop, then Beth was not discovered in the library. Otherwise, Beth was discovered in the library.
Statement c: "If Amy was discovered in the apartment building, then Mary was discovered in the shopping mall."
This statement suggests that if Amy was discovered in the apartment building, then Mary was discovered in the shopping mall.
Statement d: "If Beth was not discovered in the library, then neither was Kay."
This statement means that if Beth was not discovered in the library, then Kay was not discovered in the library either.
Let's analyze the information we have gathered from the statements:
- If Kay was not discovered in the library, then Amy was discovered in the apartment building.
- If Mary was discovered in the coffee shop, then Beth was not discovered in the library.
- If Amy was discovered in the apartment building, then Mary was discovered in the shopping mall.
- If Beth was not discovered in the library, then Kay was not discovered in the library either.
From these statements, we can conclude the following:
1. If Kay was discovered in the library, then Amy was not discovered in the apartment building.
2. If Mary was not discovered in the coffee shop, then Beth was discovered in the library.
3. If Amy was not discovered in the apartment building, then Mary was not discovered in the shopping mall.
4. If Beth was discovered in the library, then Kay was discovered in the library.
Now, let's try to match the girls with the locations:
Since we have deduced that if Mary was not discovered in the coffee shop, then Beth was discovered in the library (statement b), it means that Mary cannot be discovered in the coffee shop. Therefore, Mary must be discovered in the shopping mall (statement c).
Considering that if Mary was discovered in the shopping mall, then Amy cannot be discovered in the apartment building (statement c), it means that Amy cannot be in the apartment building. So, the only remaining option for Amy is to be discovered in the coffee shop.
Now, we know that Beth was discovered in the library (statement b). Since we have already assigned Mary and Amy to other locations, the only remaining option for Beth is to be discovered in the library.
This leaves Kay to be discovered in the shopping mall (statement c).
In conclusion:
- Amy was discovered in the coffee shop.
- Beth was discovered in the library.
- Kay was discovered in the shopping mall.
- Mary was discovered in the shopping mall.
Therefore, we have successfully matched each girl with the location in which she was discovered.