To solve the question "Which term best describes the statement: If [tex]\( x \Rightarrow y \)[/tex] and [tex]\( y \Rightarrow z \)[/tex], then [tex]\( x \Rightarrow z \)[/tex]," let's analyze each of the given options:
A. A syllogism:
- Syllogism is a logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. In this case, if [tex]\( x \)[/tex] implies [tex]\( y \)[/tex], and [tex]\( y \)[/tex] implies [tex]\( z \)[/tex], then [tex]\( x \)[/tex] logically implies [tex]\( z \)[/tex]. This matches our statement perfectly.
B. Contrapositive statement:
- The contrapositive of a statement [tex]\( p \Rightarrow q \)[/tex] is [tex]\( \neg q \Rightarrow \neg p \)[/tex], where [tex]\( \neg \)[/tex] represents negation. Our statement does not involve negation and conditional reversal, so it is not a contrapositive statement.
C. Converse statement:
- The converse of a statement [tex]\( p \Rightarrow q \)[/tex] is [tex]\( q \Rightarrow p \)[/tex]. This also does not match our statement, as it changes the direction of the implication.
D. Inverse statement:
- The inverse of a statement [tex]\( p \Rightarrow q \)[/tex] is [tex]\( \neg p \Rightarrow \neg q \)[/tex]. Similar to the contrapositive, this does not match our statement because it involves negation and does not match the given logical structure.
Given the definitions and considering the logical structure of the original statement, the term that best describes it is:
A. A syllogism.
Thus, the correct answer is:
```
1
```
A. A syllogism
