Question

If 'All Teachers are Mentors' and 'Some Mentors are Authors', is the conclusion 'All Teachers are Authors' definitely true?

• A. Yes, it is definitely true
• B. No, it is definitely false
• C. It cannot be determined
• D. Only some Teachers are Authors

Hint:

Key rule in syllogism questions:

• From \textbf{"All A are B"} and \textbf{"Some B are C"}, you \textbf{cannot conclude} that \textbf{"All A are C"}.
• Statements involving \textbf{"some"} do not guarantee universal conclusions.

Memory shortcut: \[ \textbf{All + Some } \Rightarrow \textbf{ No definite universal conclusion} \]

Answer 1

The Correct Option is C

This question is an example of syllogistic reasoning, a form of logical argument that uses deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
Step 1: Understanding the Question:
We are given two premises and a conclusion. We need to determine if the conclusion logically and necessarily follows from the premises.
Premise 1: All Teachers are Mentors.
Premise 2: Some Mentors are Authors.
Conclusion: All Teachers are Authors.
Step 2: Key Formula or Approach:
We can use a Venn diagram to visualize the relationships between the sets (Teachers, Mentors, Authors).
Step 3: Detailed Explanation:
1. Analyze Premise 1: 'All Teachers are Mentors'.
This means the set of all 'Teachers' is completely contained within the set of 'Mentors'. In a Venn diagram, the 'Teachers' circle would be inside the 'Mentors' circle.
2. Analyze Premise 2: 'Some Mentors are Authors'.
This means there is an overlap between the set of 'Mentors' and the set of 'Authors'. At least one mentor is an author. In a Venn diagram, the 'Mentors' circle and the 'Authors' circle must intersect.
3. Evaluate the Conclusion: 'All Teachers are Authors'.
Based on the premises, we know that the 'Teachers' circle is inside the 'Mentors' circle, and the 'Mentors' circle overlaps with the 'Authors' circle. However, the premises do not provide any definite information about the relationship between 'Teachers' and 'Authors'.
Two possibilities exist:
- Possibility 1: The overlap between 'Mentors' and 'Authors' might be in a region that does not include any 'Teachers'. In this case, no Teacher is an Author.
- Possibility 2: The overlap between 'Mentors' and 'Authors' might include some or all of the 'Teachers'.
Since we cannot be certain that all teachers are authors (Possibility 1 contradicts it), the conclusion is not definitely true. We also cannot say it is definitely false (Possibility 2 allows for it). Therefore, the validity of the conclusion cannot be determined from the given information.
Step 4: Final Answer:
The conclusion cannot be determined with certainty.
\[ \boxed{\text{It cannot be determined}} \]