Two statements are given, followed by two conclusions numbered I and II. 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 rats are cats.
All cats are tigers.
Conclusions:
I. Some tigers are rats.
II. All rats are tigers.
- ABoth conclusions I and II follow
- BOnly conclusion II follows
- COnly conclusion I follows
- DNeither conclusion I nor II follows
Solution & Step-by-step Explanation
Let's evaluate using Venn diagram sets:
"All rats are cats" ⟹Rats⊆Cats.
"All cats are tigers" ⟹Cats⊆Tigers.
Combining them, we get: Rats⊆Cats⊆Tigers.
Now analyzing conclusions:
Conclusion I: "Some tigers are rats." Since the whole set of rats is inside tigers, the overlapping area is non-empty. So, this follows.
Conclusion II: "All rats are tigers." Since rats are entirely contained within cats, which is inside tigers, all rats are definitely tigers. This also follows.
Thus, both conclusions I and II follow.
"All rats are cats" ⟹Rats⊆Cats.
"All cats are tigers" ⟹Cats⊆Tigers.
Combining them, we get: Rats⊆Cats⊆Tigers.
Now analyzing conclusions:
Conclusion I: "Some tigers are rats." Since the whole set of rats is inside tigers, the overlapping area is non-empty. So, this follows.
Conclusion II: "All rats are tigers." Since rats are entirely contained within cats, which is inside tigers, all rats are definitely tigers. This also follows.
Thus, both conclusions I and II follow.