Question

Statements:
I. Some cars are black
II. Some lions are cars
Conclusion:
I. Some blacks are Lions
II. No black is Lion

• A. Only I follow
• B. Only II follow
• C. Either I or II follows
• D. None follows

Hint:

\textbf{Syllogisms.} When solving syllogism problems, use Venn diagrams to visualize the relationships between the sets described in the statements. Consider all possible valid interpretations of the statements. If a conclusion must be true in all valid Venn diagrams, then it follows. If there are possibilities where a conclusion is true and where it is false, then it does not necessarily follow. For complementary conclusions like "Some A are B" and "No A are B", if neither necessarily follows individually, then "Either I or II follows" is often the correct answer.

Answer 1

The Correct Option is C

We are given two statements and two conclusions, and we need to determine which conclusion logically follows from the statements. We can use a Venn diagram to visualize the relationships described in the statements.

Statement I: Some cars are black. This implies that there is an intersection between the set of cars and the set of black things.

Statement II: Some lions are cars. This implies that there is an intersection between the set of lions and the set of cars. Combining these two statements, we can draw several possible Venn diagrams. One possibility is where the set of black things and the set of lions also have some overlap, and another possibility is where they do not overlap at all.

Possibility 1: Some blacks are lions. In this case, Conclusion I (Some blacks are Lions) is true.

Possibility 2: No blacks are lions. In this case, Conclusion II (No black is Lion) is true. It is also possible to have a scenario where some but not all blacks are lions.
Now let's analyze the conclusions:

Conclusion I: Some blacks are Lions. This conclusion is possible but not necessarily true based on the given statements.

Conclusion II: No black is Lion. This conclusion is also possible but not necessarily true based on the given statements. We have a situation where either there is some overlap between blacks and lions (Conclusion I is true), or there is no overlap between blacks and lions (Conclusion II is true). These two conclusions form a complementary pair under the given statements. They cover all possibilities regarding the relationship between blacks and lions that are consistent with the premises. Specifically, we have the form "Some A are B" and "No A are B" concerning the relationship between blacks and lions. In such cases, either one or the other must be true.

Therefore, Either Conclusion I or Conclusion II follows.