All students are learners. Some learners are not diligent. Therefore, some stude

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Question: All students are learners. Some learners are not diligent. Therefore, some students are not diligent. Is this conclusion valid?

Options:

Correct Answer: No

Solution:

The conclusion cannot be determined because while some learners are not diligent, it does not specify if those learners are students.

All students are learners. Some learners are not diligent. Therefore, some students are not diligent. Is this conclusion valid?

All students are learners. Some learners are not diligent. Therefore, some students are not diligent. Is this conclusion valid?

Step 1: Understand the first statement: 'All students are learners.' This means every student is included in the group of learners.
Step 2: Understand the second statement: 'Some learners are not diligent.' This means there are some learners who do not work hard.
Step 3: Analyze the conclusion: 'Therefore, some students are not diligent.' This suggests that there are students who do not work hard.
Step 4: Check if the learners who are not diligent are students. The second statement does not specify if the non-diligent learners are students or not.
Step 5: Since we cannot confirm that the non-diligent learners are students, we cannot conclude that some students are not diligent.

Logical Deduction – The ability to draw conclusions based on given premises and understand the relationships between different groups.
Quantifiers in Logic – Understanding the implications of universal and existential quantifiers, such as 'all' and 'some'.