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

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

Options:

  1. Yes
  2. No
  3. Only if all learners are students
  4. Only if some students are teachers

Correct Answer: Yes

Solution: 

The conclusion is valid because if all students are learners and some learners are not teachers, then some students must not be teachers.

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

Practice Questions

Q1
All students are learners. Some learners are not teachers. Therefore, some students are not teachers. Is this conclusion valid?
  1. Yes
  2. No
  3. Only if all learners are students
  4. Only if some students are teachers

Questions & Step-by-Step Solutions

All students are learners. Some learners are not teachers. Therefore, some students are not teachers. Is this conclusion valid?
  • Step 1: Understand that all students belong to the group of learners.
  • Step 2: Recognize that within the group of learners, there are some who are not teachers.
  • Step 3: Since all students are learners, and some learners are not teachers, it follows that those students who are learners could also be part of the group that is not teachers.
  • Step 4: Therefore, we can conclude that some students must not be teachers.
  • Logical Deduction – The ability to draw conclusions from given premises using logical reasoning.
  • Quantifiers in Logic – Understanding the implications of universal ('all') and existential ('some') quantifiers in logical statements.
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