Each of the following options presents a pair of premises followed by a conclusion. Three arguments are logically valid if you ignore factual absurdity and focus only on logical structure. One argument is logically wrong or doubtful. Which argument is logically incorrect?

Difficulty: Medium

Correct Answer: All liars are not thieves. All thieves are criminals. Therefore, all liars are criminals.

Explanation:


Introduction / Context:
This question belongs to the area of syllogisms and logical validity. You are given arguments that may sound absurd in everyday life, but you are explicitly asked to ignore factual absurdity and examine only the logical form. Three of the arguments follow valid patterns of deduction, while one argument has an invalid conclusion that does not follow from its premises. Your task is to identify the logically wrong or doubtful argument.


Given Data / Assumptions:

  • We treat sentences like “Birds fly in the air” or “Trees are birds” as premises, whether or not they are true in real life.
  • We focus only on whether the conclusion necessarily follows from the premises if those premises are assumed to be true.
  • Standard set notation can be used in the background: All A are B, Some A are B, etc.
  • We ignore emotional or factual judgement and examine pure structure.


Concept / Approach:
In syllogistic reasoning, an argument is valid if, whenever the premises are true, the conclusion must also be true. The actual truth of the premises does not affect validity. So even if a premise says something factually impossible, the argument can still be valid as long as the conclusion obeys the logical rules. To solve this question, translate each option into a simple logical form and then check whether the conclusion logically follows. Exactly one will fail this test.


Step-by-Step Solution:
Option A: “Birds fly in the air. Trees are birds. Therefore, trees fly in the air.” Formally: All birds fly. All trees are birds. Therefore, all trees fly. This follows the valid pattern: All B are F; All T are B; therefore, All T are F. The logic is valid, even though the premises are factually wrong. Option B: “Some boys steal. All who steal are naughty. All naughty are honest. Therefore, some boys are honest.” The form is: Some boys are thieves; All thieves are naughty; All naughty are honest. Therefore, Some boys are honest. Since the same subset of boys moves through thief to naughty to honest, this is logically valid. Option C: “All girls like dance. Some girls are Indian. All Indians are artists. Therefore, some artists like dance.” Here, some girls are both girls and Indian and all girls like dance. All Indians are artists. So some individuals are both artists and people who like dance. Therefore, some artists like dance. The structure is valid. Option D: “All liars are not thieves. All thieves are criminals. Therefore, all liars are criminals.” Interpreting “All liars are not thieves” as “No liars are thieves”, we get: All L are non thieves. All thieves are criminals. From this it does not follow that all liars are criminals, because liars could be outside the set of thieves and criminals entirely. No link is established from liars to criminals.


Verification / Alternative check:
To verify option D, construct a simple counterexample. Suppose there are liars who are not thieves and not criminals at all. The premise “All liars are not thieves” is satisfied. The premise “All thieves are criminals” is also satisfied, because any thief that exists is a criminal. Yet in this situation, not all liars are criminals, which shows the conclusion fails even when both premises are true. Therefore the argument in option D is invalid, while the others can be shown to hold for all interpretations that respect their premises.


Why Other Options Are Wrong:
Options A, B and C are logically correct even though they may contain absurd premises. In A, the structure All B are F and All T are B gives All T are F. In B, the chain Some boys are thieves, all thieves are naughty and all naughty are honest forces some boys to be honest. In C, the overlap between girls and Indians ensures that some artists are among those who like dance. None of these arguments admit a counterexample where the premises are true and the conclusion false.


Common Pitfalls:
A frequent mistake is to reject arguments because the real world content seems silly, such as trees being birds. The instructions specifically warn you to ignore factual absurdity and focus on logical form. Another pitfall is misreading “All liars are not thieves” as if it somehow means liars are criminals, which it does not. Always translate such statements carefully and check whether there is a clear link from the subject of the conclusion back through the premises.


Final Answer:
The only argument that is logically wrong or doubtful is “All liars are not thieves. All thieves are criminals. Therefore, all liars are criminals.”, which is option D.

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