In the following question, a statement is given followed by four conclusions.…
2019
In the following question, a statement is given followed by four conclusions. Choose the conclusion which logically follows from the given statement. Statement: All beggars are poor. Conclusions: I. If X is a beggar, then X is not rich. II. If X is not rich, then X is not a beggar. III. All those who are poor are beggars. IV. If X is rich, then X is not a beggar.
- A.
Only conclusion II follows.
- B.
Either conclusion III or IV follow.
- C.
Only conclusion I follows.
- D.
All conclusions follow.
Attempted by 137 students.
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Correct answer: C
Answer: Only conclusion I follows.
Reasoning:
From the statement "All beggars are poor" we get: If someone is a beggar, then that person is poor.
Conclusion I (If X is a beggar, then X is not rich) follows in ordinary interpretation because being poor excludes being rich; so a beggar will not be rich.
Conclusion II (If X is not rich, then X is not a beggar) does not follow. This is the inverse of the given implication. Counterexample: a person may be not rich but also not a beggar (for example, someone who is poor but does not beg).
Conclusion III (All those who are poor are beggars) is the converse and does not follow. Many poor people are not beggars.
Conclusion IV (If X is rich, then X is not a beggar) does not follow from the given statement alone. The formal contrapositive of "If beggar then poor" is "If not poor then not beggar." That is not the same as "If rich then not beggar" unless we assume "rich" means exactly "not poor," which is not stated. Therefore IV cannot be inferred.
Thus, only conclusion I is validly inferred from the given statement.