Is the following argument valid or invalid?P1. Start-ups with young founders always succeed.P2. Ms. Lee is the founder of a start-up.P3. Ms. Lee is young.Therefore,C. Ms. Lee's start-up will succeed.

Question

BlackTom AI · Accepted Answer

Examining the structure of the argument, we start with the given statements and the goal to assess validity.
Option a: 'a. Invalid.' This would claim that the conclusion does not logically follow from the premises. To evaluate this, consider the link: P1 says that startups with young founders always succeed. P3 confirms Ms. Lee is young, and P2 confirms Ms. Lee is the founder of a startup. From these, the predicate in P1 applies to Ms. Lee's startup, implying its success. There is a direct application of a universal claim to a specific case, which preserves truth if the premises are true. Thus, labeling this as invalid would require a flaw such as a hidden assumption or a misinterpretation of the universal statement, which is not evident here.
Option b: 'b. Valid.' This option claims the conclusion follows logically from the premises. Given P1, the class of startups with young founders is defined as always succeeding. Since Ms. Lee is a young founder of a startup (P2 and P3 together establish both conditions), the universal claim in P1 applies to her startup, yielding the conclusion that her startup will succeed. The reasoning aligns with standard universal instantiation in predicate logic: if All X are Y, and an individual a is an X, then a is Y. There is a clear and straightforward line from premises to conclusion without requiring any additional assumptions.
Now, let’s probe for potential counterpoints to strengthen understanding. Could there be a problem with P1’s scope, such as 'start-ups with young founders' meaning only certain kinds of startups or excluding Ms. Lee’s case? The statement is stated as a general rule and, in the absence of contrary information, should be applicable to Ms. Lee’s startup when the conditions are met. Therefore, no contradiction arises from the premises given.
In summary, option a would require a logical misstep or an exception to the universal claim, which isn’t present in the provided premises. Option b correctly reflects the inferential path: because the startup has a young founder (Ms. Lee) and the universal claim asserts that such startups always succeed, the conclusion follows. The reasoning relies on applying a general rule to a specific instance, which is a valid form of argument in standard logic.

ATS2946 - S1 2025 Topic 2 Quiz Question

Is the following argument valid or invalid?P1. Start-ups with young founders always succeed.P2. Ms. Lee is the founder of a start-up.P3. Ms. Lee is young.Therefore,C. Ms. Lee's start-up will succeed.

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