Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow(s) from the given statements.
Statements:
All bottles are plastics.
Some plastics are fibres.
Some fibres are glasses.
Conclusions:
(I) Some fibres are plastics.
(II) All plastics are bottles.
(III) Some glasses are fibres.
- ANone of the conclusions follows
- BOnly conclusions I and III follow
- COnly conclusion II follows
- DOnly conclusion I follows
Solution & Step-by-step Explanation
Let's evaluate each conclusion based on the given statements:
Statement analysis:
"All bottles are plastics" means Bottles ⊆ Plastics.
"Some plastics are fibres" means there is an intersection between Plastics and Fibres.
"Some fibres are glasses" means there is an intersection between Fibres and Glasses.
Evaluating Conclusions:
Conclusion I: Some fibres are plastics.
Since "Some plastics are fibres" is given, its converse "Some fibres are plastics" must logically follow. (True)
Conclusion II: All plastics are bottles.
We only know that "All bottles are plastics". The reverse statement is not necessarily true. (False)
Conclusion III: Some glasses are fibres.
Since "Some fibres are glasses" is given, its converse "Some glasses are fibres" must logically follow. (True)
Thus, only conclusions I and III follow.
Statement analysis:
"All bottles are plastics" means Bottles ⊆ Plastics.
"Some plastics are fibres" means there is an intersection between Plastics and Fibres.
"Some fibres are glasses" means there is an intersection between Fibres and Glasses.
Evaluating Conclusions:
Conclusion I: Some fibres are plastics.
Since "Some plastics are fibres" is given, its converse "Some fibres are plastics" must logically follow. (True)
Conclusion II: All plastics are bottles.
We only know that "All bottles are plastics". The reverse statement is not necessarily true. (False)
Conclusion III: Some glasses are fibres.
Since "Some fibres are glasses" is given, its converse "Some glasses are fibres" must logically follow. (True)
Thus, only conclusions I and III follow.