Syllogism – Choose the necessary conclusion from the given statements: Statements: 1) All students in my class are bright. 2) Sarla is not bright. Conclusions: I) All students in my class are bright. II) Sarla is not bright. Which alternative states what must be true about Sarla's membership in my class?

Introduction / Context:
This is a classic categorical syllogism about set membership and complements. We are told every student in the speaker’s class belongs to the set Bright, and that Sarla is outside Bright. We must infer Sarla’s relation to the set of students in my class.

Given Data / Assumptions:

• Let Class denote the set of “students in my class”.
• Premise 1: Class ⊆ Bright.
• Premise 2: Sarla ∉ Bright.
• No other information about “work hard”, or the population of non-bright persons, is provided.

Concept / Approach:
If every member of Class is Bright, then any non-Bright individual cannot be in Class (contrapositive reasoning on subset membership). This yields a definite conclusion about Sarla’s membership.

Step-by-Step Solution:
From Class ⊆ Bright, membership in Class implies membership in Bright.Given Sarla ∉ Bright, she cannot satisfy the implication’s antecedent.Therefore Sarla ∉ Class.

Verification / Alternative check:
Construct a model with Class = {x,y}, Bright = {x,y,z}, Sarla = s, and s ∉ Bright. All students in Class are bright, but Sarla is not bright; hence Sarla is outside Class. The reasoning is model-independent.

Why Other Options Are Wrong:

• “Sarla must work hard”: irrelevant; “hard work” is not in the premises.
• “Some students are not bright”: contradicts Premise 1.
• “None-bright ones are not students”: over-generalizes beyond the specific class referenced; we do not talk about all students everywhere.

Common Pitfalls:
Assuming statements about an entire universe of “students” when the premise restricts to “my class”. Also, confusing necessity with probability.

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