Difficulty: Medium
Correct Answer: Some who fail are stupid. Some criminals are stupid. Therefore, all criminals fail.
Explanation:
Introduction / Context:
This logical reasoning question tests your understanding of syllogism, that is, how conclusions follow from given premises. In such questions, you must ignore whether the statements are factually true in everyday life and instead focus only on whether the conclusion necessarily follows from the premises. The task here is to look at four short arguments and decide which one is logically wrong or doubtful, meaning that the conclusion does not follow from the premises, even if it might sound convincing at first glance.
Given Data / Assumptions:
- Each option presents a mini argument consisting of premises and a conclusion.
- Real world knowledge is ignored; only logical form matters.
- Exactly one argument is logically invalid or doubtful.
Concept / Approach:
In syllogistic reasoning, a conclusion is valid only if it follows with necessity from the premises. If the premises can be true while the conclusion is false, then the argument is invalid. Often, invalid arguments overgeneralise, for example moving from some to all, or introduce elements that are not properly linked by the premises. We therefore examine each option by asking: if all its premises are assumed true, must the conclusion also be true, or is it possible for the conclusion to be false. If it can be false, that option is the logically doubtful one.
Step-by-Step Solution:
Step 1: In option A, all books can be read, some pencils are books, and all pencils are clever. From these, it follows that some clever things, namely those pencils that are books, can be read. The conclusion that some clever things can be read therefore follows logically, so option A is valid.
Step 2: In option B, some who fail are stupid and some criminals are stupid. From this, we only know about some stupid people who overlap with those who fail and with criminals. There is no information that all criminals fail, so the conclusion that all criminals fail is an overgeneralisation and does not follow. This argument is logically invalid.
Step 3: In option C, some liars are thieves and all thieves are criminals. If some liars belong to the set of thieves, and every thief is a criminal, it necessarily follows that some liars are criminals. This is a standard valid syllogism.
Step 4: In option D, trees are green and all green things are black. Even if this is factually absurd, syllogistically, if every green thing is black and trees are green, then trees must be black. The argument is logically valid.
Verification / Alternative check:
Another way to check validity is to try to build a counter example where the premises are true but the conclusion is false. For option B, it is easy to imagine a situation where some criminals are stupid and some people who fail are stupid, but many criminals never fail in examinations or similar tasks. In that case, the premises can still hold while the conclusion that all criminals fail is clearly false. This confirms that option B is logically doubtful, while the other options remain valid under the rules of syllogism.
Why Other Options Are Wrong:
Option A is logically correct because from the premises you can safely infer that at least some clever entities can be read.
Option C is logically correct because it follows the classic pattern some A are B, all B are C, therefore some A are C.
Option D is logically correct on pure logic, since if all green things are black and trees are green, then trees must be black.
Common Pitfalls:
Many learners confuse factual truth with logical validity and reject options like D only because trees are not black in real life. Others overlook the difference between some and all, which is the trap in option B. The examination of logical form is separate from whether statements match the real world. Paying attention to quantifiers like some, all, and no is essential in syllogism questions in competitive exams. Practice in separating logical structure from content will help avoid these errors.
Final Answer:
The logically wrong or doubtful argument is Some who fail are stupid. Some criminals are stupid. Therefore, all criminals fail.
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