If the statements 'All cats are mammals' and 'Some mammals are not dogs' are tru

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Question: If the statements \'All cats are mammals\' and \'Some mammals are not dogs\' are true, which of the following must also be true?

Options:

Correct Answer: Some cats are not dogs

Solution:

Since all cats are mammals and some mammals are not dogs, it follows that some cats are not dogs.

If the statements 'All cats are mammals' and 'Some mammals are not dogs' are true, which of the following must also be true?

If the statements 'All cats are mammals' and 'Some mammals are not dogs' are true, which of the following must also be true?

Step 1: Understand the first statement: 'All cats are mammals'. This means every cat belongs to the group of mammals.
Step 2: Understand the second statement: 'Some mammals are not dogs'. This means there are certain mammals that do not belong to the group of dogs.
Step 3: Combine the information: Since all cats are mammals, and we know that some mammals are not dogs, it is possible that those mammals that are not dogs could include some cats.
Step 4: Conclude: Therefore, it must be true that some cats are not dogs, because all cats are part of the mammals, and some of those mammals are not dogs.

Logical Deduction – The ability to draw conclusions from given premises using rules of logic.
Categorical Logic – Understanding relationships between categories, such as 'all', 'some', and 'none'.