Two 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: All lotuses are roses.
All lotuses are hibiscuses.
Conclusions: I. All roses are hibiscuses.
II. Some hibiscuses are lotuses.
III. Some roses are hibiscuses.
- AOnly conclusions I and III follow
- BOnly conclusions I and II follow
- CAll of the conclusions follow
- DOnly conclusions II and III follow
Solution & Step-by-step Explanation
Let's analyze the statements using Venn diagrams or logical deduction:
Testbook
Statements:
All lotuses (L) are roses (R). (L⊆R)
All lotuses (L) are hibiscuses (H). (L⊆H)
Analysis of Conclusions:
Conclusion I: All roses are hibiscuses.
From the statements, we only know that the lotus part is common to both roses and hibiscuses. There could be roses that are not hibiscuses. Hence, this does not definitely follow.
Conclusion II: Some hibiscuses are lotuses.
Testbook
Since all lotuses are hibiscuses, it naturally follows that the region of hibiscuses containing lotuses means 'Some hibiscuses are lotuses'. This is true.
Conclusion III: Some roses are hibiscuses.
Wikipedia
Since all lotuses are roses and all lotuses are hibiscuses, the lotuses form a common intersecting region between roses and hibiscuses. Therefore, some roses are definitely hibiscuses. This is true.
Thus, only conclusions II and III follow.
Testbook
Statements:
All lotuses (L) are roses (R). (L⊆R)
All lotuses (L) are hibiscuses (H). (L⊆H)
Analysis of Conclusions:
Conclusion I: All roses are hibiscuses.
From the statements, we only know that the lotus part is common to both roses and hibiscuses. There could be roses that are not hibiscuses. Hence, this does not definitely follow.
Conclusion II: Some hibiscuses are lotuses.
Testbook
Since all lotuses are hibiscuses, it naturally follows that the region of hibiscuses containing lotuses means 'Some hibiscuses are lotuses'. This is true.
Conclusion III: Some roses are hibiscuses.
Wikipedia
Since all lotuses are roses and all lotuses are hibiscuses, the lotuses form a common intersecting region between roses and hibiscuses. Therefore, some roses are definitely hibiscuses. This is true.
Thus, only conclusions II and III follow.