While teaching in a mathematics class, a teacher gives the statement "Common Divisor of two integers is a number which divides both the given integers". The statement is a:

Question

Accepted Answer

The statement "Common Divisor of two integers is a number which divides both the given integers" is classified as a **Definition**. Here's a detailed explanation justifying why Option 2 is correct and why the other options are incorrect:

1. **Why Option 2 (Definition) is Correct:**
   - A definition is a precise statement that explains the meaning of a term or concept. In mathematics, definitions are used to establish the exact meaning of mathematical terms and concepts. The statement provided by the teacher clearly explains what a "Common Divisor" is by specifying the criteria that a number must meet to be considered a common divisor of two integers. It sets the boundaries and conditions that define the term, making it a definition.

2. **Why Option 1 (Proposition) is Incorrect:**
   - A proposition is a declarative statement that is either true or false. Propositions are often used in logical reasoning and proofs. The statement given by the teacher is not a proposition because it is not asserting a truth value or making a claim that can be evaluated as true or false. Instead, it is explaining the meaning of a term, which is characteristic of a definition.

3. **Why Option 3 (Axiom) is Incorrect:**
   - An axiom is a fundamental principle or assumption that is accepted as true without proof. Axioms serve as the starting point for further reasoning and the development of mathematical theories. The statement about a common divisor is not an axiom because it is not a foundational assumption; rather, it is a clarification of a specific mathematical concept. Definitions, unlike axioms, do not require proof or acceptance as self-evident truths.

4. **Why Option 4 (Open Sentence) is Incorrect:**
   - An open sentence is a mathematical statement containing one or more variables that do not have specific values, making the truth value of the statement undetermined until the variables are specified. The statement about a common divisor does not contain variables or an undetermined truth value. It is a clear and complete explanation of what constitutes a common divisor, fitting the criteria of a definition rather than an open sentence.

In conclusion, the statement provided by the teacher is a definition because it precisely describes the concept of a common divisor by outlining the necessary conditions a number must satisfy. This aligns with the role of definitions in mathematics, which is to provide clear and unambiguous meanings for terms and concepts.