Which of the given conclusions logically follows from the given statements?
Statements:
All apples are bananas.
No banana is a grape.
Some grapes are oranges.
Conclusions:
I. Some bananas are oranges.
II. No apple is an orange.
III. All bananas are oranges is a possibility.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Only III follows
A definite conclusion follows only if it is true in every diagram that fits the statements. A “possibility” conclusion follows if at least one such diagram makes it true.
Conclusion I (Some bananas are oranges) does not follow. Bananas are linked to oranges only through grapes, and no banana is a grape, so the left diagram, in which no banana is an orange, fits all three statements.
Conclusion II (No apple is an orange) does not follow. Nothing stops the oranges from taking in all the bananas, and the apples with them, as in the right diagram.
Conclusion III (All bananas are oranges is a possibility) follows. The right diagram fits every statement and has all the bananas inside the oranges.