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All teachers are educated. Some educated people are not teachers. Therefore, som

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Question: All teachers are educated. Some educated people are not teachers. Therefore, some people who are not teachers are educated. Is this conclusion valid? (2023)

Options:

  1. Yes
  2. No
  3. Only if all educated people are teachers
  4. Only if some teachers are educated

Correct Answer: Yes

Exam Year: 2023

Solution: 

The conclusion is valid. The premises allow for the existence of educated people who are not teachers.

All teachers are educated. Some educated people are not teachers. Therefore, som

Practice Questions

Q1
All teachers are educated. Some educated people are not teachers. Therefore, some people who are not teachers are educated. Is this conclusion valid? (2023)
  1. Yes
  2. No
  3. Only if all educated people are teachers
  4. Only if some teachers are educated

Questions & Step-by-Step Solutions

All teachers are educated. Some educated people are not teachers. Therefore, some people who are not teachers are educated. Is this conclusion valid? (2023)
  • Step 1: Understand the first statement: 'All teachers are educated.' This means every teacher has an education.
  • Step 2: Understand the second statement: 'Some educated people are not teachers.' This means there are educated people who do not teach.
  • Step 3: Analyze the conclusion: 'Some people who are not teachers are educated.' This suggests that among those who are not teachers, there are some who are educated.
  • Step 4: Connect the statements: Since all teachers are educated and some educated people are not teachers, it is possible that those educated people who are not teachers are part of the group of people who are not teachers.
  • Step 5: Determine if the conclusion follows: Since we have established that there are educated people who are not teachers, it confirms that some people who are not teachers can indeed be educated.
  • Logical Deduction – The ability to draw conclusions from given premises using logical reasoning.
  • Quantifiers in Logic – Understanding the implications of universal ('all') and particular ('some') quantifiers in logical statements.
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