Statements: A. All the students in my class are intelligent. B. Rashmi is not intelligent. Which conclusion necessarily follows?

Introduction / Context:This question examines contrapositive reasoning. From a universal statement about all students in a class, and a fact about Rashmi, we must deduce Rashmi’s membership relative to that class.

Given Data / Assumptions:

• A: If x is a student of my class, then x is intelligent.
• B: Rashmi is not intelligent.
• No other information about Rashmi’s skills or roles.

Concept / Approach:Use the contrapositive of the universal conditional. From “Student ⇒ Intelligent,” we obtain “Not Intelligent ⇒ Not a Student (of my class).” This is a logically equivalent form and is guaranteed to hold if the original universal holds.

Step-by-Step Solution:

Verification / Alternative check:Test the options against models: If any model satisfies A and B but falsifies the conclusion, discard it. There is no such model; in every case, Rashmi must be outside the set “students of my class.”

Why Other Options Are Wrong:

Common Pitfalls:Confusing converse (Intelligent ⇒ Student) with contrapositive; adding irrelevant real-world assumptions.

Final Answer:Rashmi is not a student of my class.