Difficulty: Easy
Correct Answer: Only conclusion I follows
Explanation:
Introduction / Context:
This problem is a classic example of a syllogism in logical reasoning. You are given a general rule about a group, in this case all boys, and then a specific individual who belongs to that group. Your task is to decide whether each conclusion about that individual follows logically from the general rule. This type of question checks whether you can correctly apply universal statements to particular instances without being confused by contradictory options.
Given Data / Assumptions:
Concept / Approach:
The key concept is that a universal affirmative statement of the form “All A are B” means every member of set A is guaranteed to be in set B. When we are told that a specific individual belongs to set A, we can directly conclude that the individual also belongs to set B. Any conclusion that directly contradicts this must be rejected. This is a direct application of basic deductive reasoning, where we move from the general to the particular.
Step-by-Step Solution:
Step 1: Interpret the given universal statement. “All boys are tall” means that for every person x, if x is a boy, then x is tall. No exception is allowed by this statement.
Step 2: Note the specific information about Rajiv. We are explicitly told that Rajiv is a boy. Therefore Rajiv belongs to the set of boys.
Step 3: Apply the universal rule to Rajiv. Since Rajiv is in the set of boys and all members of that set are tall, it must follow that Rajiv is tall.
Step 4: Evaluate Conclusion I. It states exactly what we deduced: Rajiv is tall. Therefore Conclusion I logically follows from the given statement.
Step 5: Evaluate Conclusion II. It says Rajiv is not tall. This directly contradicts the result that Rajiv must be tall. A valid conclusion can never directly contradict a logically necessary result of the premises, so Conclusion II does not follow.
Verification / Alternative check:
You can verify this with a simple substitution example. Imagine a group where every boy is at least 180 cm tall. If we now say Rajiv is a boy in that group, it is impossible for Rajiv to be shorter than 180 cm. Any statement that says “Rajiv is not tall” is inconsistent with the given rule. This confirms that only the first conclusion aligns with the premises and the second is impossible if the statements are true.
Why Other Options Are Wrong:
Option b: “Only conclusion II follows” is wrong because it asserts the exact opposite of what the premises demand.
Option c: “Both conclusion I and conclusion II follow” is impossible because two directly contradictory conclusions cannot both be correct at the same time.
Option d: “Neither conclusion I nor conclusion II follows” is incorrect because we have seen that Conclusion I is a direct and compulsory result of the given statement.
Option e: “The relationship cannot be determined” is also incorrect. The relationship is fully determined by the universal statement and the classification of Rajiv as a boy.
Common Pitfalls:
Learners sometimes think that because they see both “Rajiv is tall” and “Rajiv is not tall”, the answer must be “either or neither”. However, syllogism questions are not about what could be true in some world, but what must be true given the premises. Since the given statement leaves no room for any boy to be not tall, the conclusion that Rajiv is tall is unavoidable. Never treat mutually exclusive conclusions as both correct when the premises clearly support only one of them.
Final Answer:
Only conclusion I follows from the given statement.
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