Identify the correct option regarding the statements & conclusions given:
Statements:
1. All guitars are instruments.
2. All instruments are sitars.
Conclusions:
1. All sitars are instruments.
2. All guitars are sitars.
- AOnly Conclusion 1 follows.
- BOnly Conclusion 2 follows.
- CBoth Conclusions 1 and 2 follow.
- DNeither Conclusion 1 nor 2 follows.
Solution & Step-by-step Explanation
Let's analyze using Venn diagrams or logical inclusion:
* "All guitars are instruments" means .
* "All instruments are sitars" means .
Combining both, we get: .
Now evaluate the conclusions:
* Conclusion 1: "All sitars are instruments." This is not necessarily true because the set of sitars can be larger than instruments. Only "Some sitars are instruments" definitely follows. Thus, Conclusion 1 does not follow.
* Conclusion 2: "All guitars are sitars." Since , this is definitely true. Thus, Conclusion 2 follows.
* "All guitars are instruments" means .
* "All instruments are sitars" means .
Combining both, we get: .
Now evaluate the conclusions:
* Conclusion 1: "All sitars are instruments." This is not necessarily true because the set of sitars can be larger than instruments. Only "Some sitars are instruments" definitely follows. Thus, Conclusion 1 does not follow.
* Conclusion 2: "All guitars are sitars." Since , this is definitely true. Thus, Conclusion 2 follows.