Statements:All symbols are letters.Some letters are numbers.No numbers...
Given Statements:
All symbols are letters.
Some letters are numbers.
No numbers are a digit.
Conclusion:
I. All letters are digits is a possibility.
II. Some symbols are digits is a possibility.
Explanation:
To find out whether the conclusions follow or not, we need to check the validity of the statements.
From the first statement, "All symbols are letters", we can infer that symbols are a subset of letters. So, whatever is true for letters will also be true for symbols.
From the second statement, "Some letters are numbers", we can infer that there are some letters which are also numbers.
From the third statement, "No numbers are a digit", we can infer that there is no number which is a digit.
Now, let's check the conclusions:
Conclusion I: All letters are digits is a possibility.
This conclusion is not valid because we know that there are some letters which are numbers but no numbers are digits. So, we cannot say that all letters are digits.
Conclusion II: Some symbols are digits is a possibility.
This conclusion is also not valid because we cannot directly infer that some symbols are digits. Even though symbols are a subset of letters and some letters are numbers, we cannot say that some symbols are digits because no numbers are digits.
Therefore, only conclusion II does not follow.
Hence, the correct answer is option B - If only conclusion II follows.