Question

Statements:
• Some cashmere jackets are fashionable.
• Some cashmere jackets are not suede jackets.
• No suede jacket is fashionable.
Which of the following conclusions is correct?

• A. Some fashionable jackets are not suede jackets
• B. All cashmere jackets are fashionable
• C. Some suede jackets are cashmere jackets
• D. No cashmere jacket is fashionable

Hint:

In logic, if "No A is B," then "No B is A" and "Some B is not A" are always valid deductions. Since No Suede is Fashionable, it is a fact that any Fashionable item you pick will not be Suede.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
This is a syllogism problem that can be solved using Venn diagrams to represent the relationships between the three sets: Cashmere Jackets (C), Fashionable Jackets (F), and Suede Jackets (S).

Step 2: Analyzing the Statements
1. "Some cashmere jackets are fashionable": There is an intersection between set C and set F. 2. "No suede jacket is fashionable": Set S and set F are completely disjoint (they do not touch). 3. "Some cashmere jackets are not suede jackets": At least one part of C is outside of S.

Step 3: Evaluating the Conclusions
1. Conclusion (A): Since "No suede jacket is fashionable," it logically follows that any jacket that is fashionable cannot be a suede jacket. Therefore, all fashionable jackets are "not suede jackets." If all are not, then "some" are certainly not. This conclusion is universally true based on the third statement. 2. Conclusion (B): The statement only says "some" cashmere jackets are fashionable, so we cannot conclude "all" are. 3. Conclusion (C): While it's possible for cashmere and suede sets to overlap, the statements do not provide enough information to guarantee that they must overlap. 4. Conclusion (D): This contradicts the first statement ("Some cashmere jackets are fashionable").

Step 4: Final Answer
The correct conclusion is (A).