Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow from the statements. Statements: Some Ducks are Cats. All Cats are Rats. Conclusions:I. All Rats are Ducks.II. No Rat is a Duck.
- ABoth conclusions I and II follow.
- BOnly conclusion I follows.
- CNeither conclusion I nor II follows.
- DOnly conclusion II follows.
Solution & Step-by-step Explanation
Let's analyze the statements using standard set logic: "Some Ducks are Cats" means there is an intersection between the Ducks set and the Cats set."All Cats are Rats" means the entire Cats set is contained inside the Rats set.Now, let's evaluate the conclusions:Conclusion I: "All Rats are Ducks." This is not necessarily true because the Rats set is larger and only the part containing Cats is guaranteed to overlap with Ducks. Thus, conclusion I does not follow.Conclusion II: "No Rat is a Duck." Since all Cats are Rats, and some Ducks are Cats, those specific Cats are both Rats and Ducks. Therefore, there is definitely an overlap between Rats and Ducks, making "No Rat is a Duck" definitely false.Thus, neither conclusion I nor II follows.