Statements All green are blue. All blue are white. Conclusions I) Some blue…
2023
Statements
All green are blue.
All blue are white.
Conclusions
I) Some blue are green.
II) Some white are green.
III) Some green are not white.
IV) All white are blue.
- A.
Only I and II follow
- B.
Only II and III follow
- C.
Only I and III follow
- D.
Only I and IV follow
Attempted by 294 students.
Show answer & explanation
Correct answer: A
Key fact: From the premises, every green is a blue and every blue is a white, so every green is a white.
Conclusion I (Some blue are green): True — if at least one green exists, that green is also a blue, so there exists a blue that is green. (Note: this uses the usual existential assumption that a category mentioned actually has at least one member.)
Conclusion II (Some white are green): True — if at least one green exists, that green is also white because all green are white, so there exists a white that is green.
Conclusion III (Some green are not white): False — the premises imply every green is white, so no green can be not white.
Conclusion IV (All white are blue): False — the premises give all blue are white, but that does not imply all white are blue; whites may include elements that are not blue.
Answer: Only the conclusions "Some blue are green" and "Some white are green" follow, under the usual assumption that at least one green exists.