Question:
Consider the following Statements:
- No cats are dogs.
- All dogs are animals.
- Some animals are not cats.
Based on the above statements, which is true?
Options:
(1) Some cats are animals.
(2) No dogs are cats.
(3) All animals are dogs.
(4) All dogs are cats.
Solution:
Analysis of Statements:
"No cats are dogs"
This means there is no overlap between cats and dogs.
"All dogs are animals"
This means every dog is an animal.
"Some animals are not cats"
This implies that there are animals that do not belong to the category of cats.
Evaluating Options:
Option (1): Some cats are animals.
This is incorrect because it contradicts Statement 1, which states that no cats are dogs (and all dogs are animals).
Option (2): No dogs are cats.
This is correct because it directly agrees with Statement 1.
Option (3): All animals are dogs.
This is incorrect because Statement 2 only states that all dogs are animals, not that all animals are dogs.
Option (4): All dogs are cats.
This is incorrect because Statement 1 explicitly states that no cats are dogs.
Answer: (2) No dogs are cats.