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

Concept:
This question is based on syllogistic reasoning, which involves drawing logical conclusions from given statements. In syllogism problems, we analyze relationships between different groups or categories using logical rules. Important principles used in syllogism:

• The statement "All A are B" means every member of set A belongs to set B.
• The statement "Some B are C" means at least one member of set B belongs to set C.
• However, a statement about "some" elements cannot be generalized to represent "all" elements.

Step 1: Analyze the first statement.
\[ \text{All Teachers are Mentors} \] This means the entire group of Teachers lies within the group Mentors. \[ \text{Teachers} \subseteq \text{Mentors} \]
Step 2: Analyze the second statement.
\[ \text{Some Mentors are Authors} \] This means that only a portion of Mentors are Authors. It does not imply that all Mentors are Authors.

Step 3: Check the conclusion.
The conclusion states: \[ \text{All Teachers are Authors} \] But from the given information, we only know that:

• Teachers belong to the group of Mentors.
• Some Mentors are Authors.

It is possible that:

• The Mentors who are Authors are not Teachers.
• Teachers may belong to the portion of Mentors that are not Authors.

Therefore, the conclusion cannot be guaranteed.
Step 4: Logical interpretation using set relationships.
\[ \text{Teachers} \subseteq \text{Mentors} \] \[ \text{Some Mentors} \subseteq \text{Authors} \] But there is no definite relation that confirms: \[ \text{Teachers} \subseteq \text{Authors} \] Hence, the conclusion is not logically certain.
Step 5: Selecting the correct answer.
\[ \boxed{\text{It cannot be determined}} \]