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If a person is a teacher, then they are educated. Sarah is not educated. Can we

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Question: If a person is a teacher, then they are educated. Sarah is not educated. Can we conclude that Sarah is not a teacher?

Options:

  1. Yes
  2. No
  3. Only if she is not a tutor
  4. Cannot be determined

Correct Answer: Yes

Solution: 

The conclusion is valid because if being a teacher implies being educated, then not being educated means Sarah cannot be a teacher.

If a person is a teacher, then they are educated. Sarah is not educated. Can we

Practice Questions

Q1
If a person is a teacher, then they are educated. Sarah is not educated. Can we conclude that Sarah is not a teacher?
  1. Yes
  2. No
  3. Only if she is not a tutor
  4. Cannot be determined

Questions & Step-by-Step Solutions

If a person is a teacher, then they are educated. Sarah is not educated. Can we conclude that Sarah is not a teacher?
  • Step 1: Understand the statement 'If a person is a teacher, then they are educated.' This means that all teachers are educated.
  • Step 2: Recognize that Sarah is not educated. This means she does not meet the requirement of being educated.
  • Step 3: Since all teachers must be educated, and Sarah is not educated, she cannot be a teacher.
  • Step 4: Therefore, we can conclude that Sarah is not a teacher.
  • Logical Implication – Understanding that if A implies B (if a person is a teacher, then they are educated), then not B (not being educated) implies not A (not being a teacher).
  • Contrapositive Reasoning – Recognizing that the contrapositive of a statement is logically equivalent to the original statement.
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