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:
All calculators are dustbins.
All complexes are dustbins.
Some adamants are cameras.
Conclusions:
I. Some calculators are complexes.
II. Some dustbins are calculators.
III. Some dustbins are adamants.
- ABoth conclusions I and II follow
- BBoth conclusions II and III follow
- COnly conclusion II follows
- DOnly conclusion III follows
Solution & Step-by-step Explanation
Let's test each conclusion using the rules of Syllogism:
Conclusion I: Some calculators are complexes.
From the statements, both calculators and complexes are subsets inside the larger set of dustbins. However, there is no direct or definitive connection given between calculators and complexes. Therefore, it does not necessarily follow.
Conclusion II: Some dustbins are calculators.
The first statement tells us that "All calculators are dustbins." By immediate conversion, we can definitively say that "Some dustbins are calculators." Therefore, Conclusion II follows.
Conclusion III: Some dustbins are adamants.
There is no link provided in the statements between dustbins (or calculators/complexes) and adamants/cameras. Hence, Conclusion III does not follow.
Thus, only conclusion II follows.
Conclusion I: Some calculators are complexes.
From the statements, both calculators and complexes are subsets inside the larger set of dustbins. However, there is no direct or definitive connection given between calculators and complexes. Therefore, it does not necessarily follow.
Conclusion II: Some dustbins are calculators.
The first statement tells us that "All calculators are dustbins." By immediate conversion, we can definitively say that "Some dustbins are calculators." Therefore, Conclusion II follows.
Conclusion III: Some dustbins are adamants.
There is no link provided in the statements between dustbins (or calculators/complexes) and adamants/cameras. Hence, Conclusion III does not follow.
Thus, only conclusion II follows.