Question Details

Statements: I. Some cars are black II. Some lions are cars

Conclusion I. Some blacks are Lions II. No black is Lion

Options

A

Only I follow

B

Only II follow

C

Either I or II follows

D

None follows

Show Answer

Correct Answer :

Option C

Either I or II follows

Solution :

The correct option is Either I or II follows.

To understand why this is the correct choice, let us analyze the given statements and conclusions step-by-step:

Step 1: Analyze the Statements
Statement I: "Some cars are black" means there is an intersection between the group of "cars" and the group of "black" items.
Statement II: "Some lions are cars" means there is an intersection between the group of "lions" and the group of "cars".

Step 2: Determine the Relationship between "Black" and "Lions"
The statements establish a relationship between "cars and black" and between "lions and cars". However, there is no direct information given about the relationship between "black" and "lions".
Because there is no direct link, two possibilities exist:
1. The group of "black" items and "lions" may overlap (Some blacks are lions).
2. The group of "black" items and "lions" may not overlap at all (No black is a lion).

Step 3: Evaluate the Conclusions
Conclusion I: "Some blacks are Lions" (This is possible but not definitely true).
Conclusion II: "No black is Lion" (This is also possible but not definitely true).
Since both conclusions are individually uncertain, neither can be said to follow definitely on its own.

Step 4: Check for the "Either-Or" Conditions
In syllogisms, an "Either-Or" choice applies when a pair of conclusions satisfies the following three conditions:
1. Both conclusions contain the same subject and predicate (here, "black" and "Lions").
2. Both conclusions are individually invalid or doubtful based on the statements.
3. The two conclusions form a complementary pair. A complementary pair typically consists of:
- "Some" + "No" (which we have here: "Some blacks are Lions" and "No black is Lion").

Since all three conditions are satisfied, it is guaranteed that either Conclusion I is true or Conclusion II is true. Therefore, the correct choice is Either I or II follows.

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