Questions: What is the negation of "Some A are B"?
Choose the correct answer below.
A. Not all B are A.
B. No A are B.
C. Not all A are B.
D. No B are A.
Transcript text: What is the negation of "Some A are B"?
Choose the correct answer below.
A. Not all B are A.
B. No A are B.
C. Not all A are B.
D. No B are A.
Solution
The answer is B: No A are B.
Explanation for each option:
A. Not all B are A. - This statement is not the correct negation of "Some A are B." It suggests that there are some B that are not A, which does not directly negate the original statement.
B. No A are B. - This is the correct negation. The original statement "Some A are B" means that there is at least one A that is also B. The negation would be that there are no A that are B, which is exactly what this option states.
C. Not all A are B. - This statement implies that there are some A that are not B, which does not negate the original statement. The original statement can still be true if not all A are B.
D. No B are A. - This statement suggests that there are no B that are A, which is not the correct negation of "Some A are B." It focuses on the wrong relationship.
In summary, the correct negation of "Some A are B" is "No A are B."