To determine 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 option:
A. A syllogism: Syllogism is a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises). For example, if we have:
1. [tex]\(x \Rightarrow y\)[/tex] (Premise 1)
2. [tex]\(y \Rightarrow z\)[/tex] (Premise 2)
From these premises, we can conclude [tex]\(x \Rightarrow z\)[/tex]. This is an example of a logical syllogism.
B. Converse statement: The converse of a statement [tex]\(p \Rightarrow q\)[/tex] is [tex]\(q \Rightarrow p\)[/tex]. This option does not describe the given statement correctly because we are not reversing the implication.
C. Inverse statement: The inverse of a statement [tex]\(p \Rightarrow q\)[/tex] is [tex]\(\neg p \Rightarrow \neg q\)[/tex]. This option also does not describe the given statement correctly because we are not negating the implications.
D. Contrapositive statement: The contrapositive of a statement [tex]\(p \Rightarrow q\)[/tex] is [tex]\(\neg q \Rightarrow \neg p\)[/tex]. This option does not describe the given statement either because the contrapositive involves negating and reversing the original implication.
Given these definitions, it is clear that the correct term to describe the statement "If [tex]\( x \Rightarrow y \)[/tex] and [tex]\( y \Rightarrow z \)[/tex], then [tex]\( x \Rightarrow z \)[/tex]" is a syllogism.
Therefore, the best term that describes the statement is:
A. A syllogism
