The statement provided is: "If [tex]\( p = q \)[/tex] and [tex]\( q = r \)[/tex], then [tex]\( p \Rightarrow r \)[/tex]."
Let's analyze this step by step:
1. Understanding the Statement:
- We are given two premises:
- [tex]\( p = q \)[/tex]
- [tex]\( q = r \)[/tex]
- We need to conclude [tex]\( p \Rightarrow r \)[/tex].
2. Transitive Property:
- This statement leverages the transitive property of equality in logic and mathematics.
- The transitive property suggests that if [tex]\( p = q \)[/tex] and [tex]\( q = r \)[/tex], then it logically follows that [tex]\( p = r \)[/tex].
3. Conclusion:
- From the premises, using the transitive property, we conclude [tex]\( p = r \)[/tex].
- The implication [tex]\( p \Rightarrow r \)[/tex] means that p being r follows logically from the premises.
4. Logical Term:
- The structure "If [tex]\( p = q \)[/tex] and [tex]\( q = r \)[/tex], then [tex]\( p \Rightarrow r \)[/tex]" follows a form of logical reasoning.
- This form of reasoning is classically termed as a "syllogism."
- A syllogism is a kind of logical argument where a conclusion is inferred from two given or assumed propositions or premises.
Therefore, the term that best describes the statement is:
A. A syllogism
