Question

Statements: Some rats are cows. All cows are animals.
Conclusions:
I. All rats are animals
II. Some animals are rats

• A. Only Conclusion I follows
• B. Only Conclusion II follows
• C. Both Conclusions I and II follow
• D. Neither Conclusion I nor Conclusion II follows

Hint:

In syllogisms, remember that “All A are B” does not mean “All B are A.” Use Venn diagrams to test whether a conclusion is necessarily true in all cases allowed by the premises.

Answer 1

The Correct Option is B

Step 1: Represent statements in standard form.
From “Some rats are cows” and “All cows are animals” we can deduce:

• Some rats are cows.
• All cows are animals \(\Rightarrow\) the cows mentioned are part of the animals set.

Step 2: Test Conclusion I — “All rats are animals.”
From the statements, only some rats are cows, and those cows are animals. There could be rats outside the cow group that are not known to be animals (based on the given premises). So, “All rats are animals” cannot be concluded.

Step 3: Test Conclusion II — “Some animals are rats.”
Since some rats are cows and all cows are animals, these “some rats” are definitely animals. This makes “Some animals are rats” logically true.

\[ \boxed{\text{Only\ Conclusion\ II\ follows.}} \]