Exclusive choice reasoning: “Ram will either buy a car or a flat.” Identify the conclusion that must follow under an exclusive-or interpretation (exactly one of the two is purchased).

Difficulty: Easy

Correct Answer: Ram did not bought Car so he must have bought Flat.

Explanation:


Introduction / Context:
In many test items, “either … or …” is taken as an exclusive-or (XOR): exactly one of the two alternatives holds, not both. We are told: “Ram will either buy a car or a flat.” We must find which conclusion necessarily follows.


Given Data / Assumptions:

  • Interpret “either … or …” as exclusive: exactly one of {Car, Flat} is true.
  • No other purchases beyond this pair are relevant.


Concept / Approach:
Under XOR, the two statements are mutually exclusive and collectively exhaustive. Therefore, if we learn one is false, the other must be true. Conversely, if we learn one is true, we may conclude the other is false. The only option that gives a must-follow conclusion independent of which item he actually chose is the conditional negation version.


Step-by-Step Solution:

1) Encode: C = “bought car”; F = “bought flat”.2) Given: exactly one of C, F is true.3) From not C, we must infer F (because one must hold).4) Therefore, “Ram did not buy car so he must have bought flat” is necessarily true.


Verification / Alternative check:
Truth cases: (C, not F) or (not C, F). In the second case, not C implies F immediately; in the first, the statement’s antecedent is false, so no contradiction arises.


Why Other Options Are Wrong:

  • “Ram bought a flat so he will not buy a car.” This can be concluded if we already know he bought a flat, but it is not a universal conclusion derived solely from the original statement without that extra fact.
  • “Ram bought a car so he will not buy a flat.” Same issue as above—requires extra fact.
  • “None of these.” Incorrect because one option (the “not car → flat” conditional) is a necessary consequence of XOR.


Common Pitfalls:
Confusing inclusive-or with exclusive-or. Standard test convention favors exclusive unless context suggests otherwise.


Final Answer:
Ram did not bought Car so he must have bought Flat.

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