All A are B. Some B are C. Does it necessarily follow that Some A are C?

All A are B. Some B are C. Does it necessarily follow that Some A are C?

• A. Yes
• B. No
• C. Not necessarily
• D. Cannot be determined

Answer: (C)

In set reasoning, All A are B means every element of A is also an element of B. Some B are C means there exists at least one element that is in both B and C. Because A is entirely within B, it doesn’t guarantee that the part of B that overlaps with C actually lies inside A. So you cannot conclude that some A are C. For a concrete look, let A = {1}, B = {1, 2}, and C = {2}. All A are B holds, and some B are C holds (the element 2), but A and C share no elements, so no A is C. Therefore the conclusion does not necessarily follow.

In set reasoning, All A are B means every element of A is also an element of B. Some B are C means there exists at least one element that is in both B and C. Because A is entirely within B, it doesn’t guarantee that the part of B that overlaps with C actually lies inside A. So you cannot conclude that some A are C. For a concrete look, let A = {1}, B = {1, 2}, and C = {2}. All A are B holds, and some B are C holds (the element 2), but A and C share no elements, so no A is C. Therefore the conclusion does not necessarily follow.