Let's analyze the statement: "If [tex]\(x \Rightarrow y\)[/tex] and [tex]\(y \Rightarrow z\)[/tex], then [tex]\(x \Rightarrow z\)[/tex]."
This statement is a form of logical reasoning known in logic and philosophy. This type of reasoning involves a sequence of statements or premises that lead to a conclusion.
1. Understanding each option:
- A. A syllogism: In formal logic, a syllogism is a kind of logical argument where a conclusion is inferred from two premises. An example would be "If all humans are mortal and Socrates is a human, then Socrates is mortal."
- B. Converse statement: The converse of a statement [tex]\(p \Rightarrow q\)[/tex] is [tex]\(q \Rightarrow p\)[/tex]. It involves swapping the hypothesis and the conclusion.
- C. Contrapositive statement: The contrapositive of a statement [tex]\(p \Rightarrow q\)[/tex] is [tex]\(\neg q \Rightarrow \neg p\)[/tex]. It involves negating both the hypothesis and the conclusion, and then reversing them.
- D. Inverse statement: The inverse of a statement [tex]\(p \Rightarrow q\)[/tex] is [tex]\(\neg p \Rightarrow \neg q\)[/tex]. It involves negating both the hypothesis and the conclusion.
2. Applying the definitions:
- The statement given is "If [tex]\(x \Rightarrow y\)[/tex] and [tex]\(y \Rightarrow z\)[/tex], then [tex]\(x \Rightarrow z\)[/tex]." This fits the pattern of logical inference where two premises lead to a conclusion.
- This does not fit the pattern of a converse, contrapositive, or inverse statement as defined above.
3. Conclusion:
- The term that best describes this type of logical reasoning is a syllogism, because it involves drawing a conclusion from two premises: [tex]\(x \Rightarrow y\)[/tex] and [tex]\(y \Rightarrow z\)[/tex], leading to [tex]\(x \Rightarrow z\)[/tex].
Therefore, the correct term to describe the statement is:
A. A syllogism
