The two statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some animals are tigers.
All tigers are vertebrates.
Conclusions:
I. All vertebrates are tigers.
II. Some vertebrates are animals.
- ABoth conclusion I & II follow
- BOnly conclusion II follows
- COnly conclusion I follows
- DNeither conclusion I nor II follows
Solution & Step-by-step Explanation
Let's analyze the statements using Venn diagrams or logical relations:
Statement 1: "Some animals are tigers." This means there is an intersection between the set of 'Animals' and the set of 'Tigers'.
Statement 2: "All tigers are vertebrates." This means the entire set of 'Tigers' is inside the set of 'Vertebrates'.
Now, let's check the conclusions:
Conclusion I: "All vertebrates are tigers." From Statement 2, we know all tigers are vertebrates, but the reverse ("All vertebrates are tigers") is not necessarily true. Thus, Conclusion I does not logically follow.
Conclusion II: "Some vertebrates are animals." Since all tigers are vertebrates, and some animals are tigers, the portion of animals that are tigers must also be vertebrates. Therefore, there is definitely an intersection between 'Vertebrates' and 'Animals'. Thus, Conclusion II logically follows.
Hence, only conclusion II follows.
Statement 1: "Some animals are tigers." This means there is an intersection between the set of 'Animals' and the set of 'Tigers'.
Statement 2: "All tigers are vertebrates." This means the entire set of 'Tigers' is inside the set of 'Vertebrates'.
Now, let's check the conclusions:
Conclusion I: "All vertebrates are tigers." From Statement 2, we know all tigers are vertebrates, but the reverse ("All vertebrates are tigers") is not necessarily true. Thus, Conclusion I does not logically follow.
Conclusion II: "Some vertebrates are animals." Since all tigers are vertebrates, and some animals are tigers, the portion of animals that are tigers must also be vertebrates. Therefore, there is definitely an intersection between 'Vertebrates' and 'Animals'. Thus, Conclusion II logically follows.
Hence, only conclusion II follows.