Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some diamonds are stones.
Some stones are hard.
All hard are rocks.
Conclusions:
I. Some stones are diamonds.
II. All stones are hard.
III. Some hard are rocks.
- AAll the conclusions follow
- BOnly conclusions I and II follow
- COnly conclusions II and III follow
- DOnly conclusions I and III follow
Solution & Step-by-step Explanation
Let's test each conclusion based on the given statements:
Conclusion I: Some stones are diamonds.
From statement 1: "Some diamonds are stones." Its immediate converse is "Some stones are diamonds." Therefore, this conclusion follows.
Conclusion II: All stones are hard.
From statement 2: "Some stones are hard." We cannot infer that all stones are hard. Therefore, this conclusion does not follow.
Conclusion III: Some hard are rocks.
From statement 3: "All hard are rocks." Since the entire set of 'hard' items is inside 'rocks', any subset of 'hard' items is also a part of 'rocks'. Hence, "Some hard are rocks" follows.
Thus, only conclusions I and III follow.
Conclusion I: Some stones are diamonds.
From statement 1: "Some diamonds are stones." Its immediate converse is "Some stones are diamonds." Therefore, this conclusion follows.
Conclusion II: All stones are hard.
From statement 2: "Some stones are hard." We cannot infer that all stones are hard. Therefore, this conclusion does not follow.
Conclusion III: Some hard are rocks.
From statement 3: "All hard are rocks." Since the entire set of 'hard' items is inside 'rocks', any subset of 'hard' items is also a part of 'rocks'. Hence, "Some hard are rocks" follows.
Thus, only conclusions I and III follow.