Some students are diligent. All diligent people succeed. Therefore, some student

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Question: Some students are diligent. All diligent people succeed. Therefore, some students succeed. Is this conclusion valid? (2023)

Options:

Correct Answer: Yes

Exam Year: 2023

Solution:

The conclusion is valid. If some students are diligent and all diligent people succeed, then it follows that some students succeed.

Some students are diligent. All diligent people succeed. Therefore, some students succeed. Is this conclusion valid? (2023)

Some students are diligent. All diligent people succeed. Therefore, some students succeed. Is this conclusion valid? (2023)

Step 1: Identify the first statement: 'Some students are diligent.' This means there is at least one student who is diligent.
Step 2: Identify the second statement: 'All diligent people succeed.' This means every person who is diligent will succeed.
Step 3: Combine the two statements: Since some students are diligent and all diligent people succeed, it means that the diligent students will also succeed.
Step 4: Conclusion: Since there is at least one diligent student and all diligent students succeed, it follows that at least one student (the diligent one) succeeds.

Logical Reasoning – The question tests the ability to understand and apply logical syllogisms, specifically the relationship between premises and conclusions.
Quantifiers in Logic – The use of quantifiers such as 'some' and 'all' is crucial in determining the validity of the conclusion based on the premises.