Which term best describes the statement given below? If x -> y and y -> z, then x -> z.
Options
- AContrapositive
- BConverse
- CInverse
- DSyllogism
Answer
The term that best describes the statement is D. Syllogism, as it reflects the logical progression that if x -> y and y -> z, then x -> z is true. This follows the principle of transitive reasoning in logic. Therefore, the correct answer is D.
Explanation
The given statement is: If x -> y and y -> z, then x -> z. This statement represents a core principle in formal logic known as a Syllogism (specifically a hypothetical syllogism). To understand it better, here’s a step-by-step breakdown: Understanding the Implications: The statement can be understood as: if x leads to y and y leads to z, then it logically follows that x must lead to z. This is known as the transitive property in logic and reasoning. Examining the Options: A. Contrapositive: This term refers to a statement that negates both the hypothesis and the conclusion and flips them, such as ¬y -> ¬x. This is not what is being described. B. Converse: This refers to flipping the hypothesis and conclusion of the original conditional statement (y -> x). This does not apply here. C. Inverse: This involves negating both the hypothesis and conclusion without flipping them (¬x -> ¬y). D. Syllogism: This is the correct term. It captures the essence of a deductive argument where a conclusion is drawn from two given or assumed propositions (premises). Thus, the statement takes the form of a syllogism, demonstrating the logical connectivity among the conditions. Hence the answer is D. Syllogism.