Which term best describes the statement given below?
If x y and y z, then x z.
A. Contrapositive
B. Converse
C. Inverse
D. Syllogism
The Correct Answer and Explanation is :
The correct answer is D. Syllogism.
Explanation:
A syllogism is a form of logical reasoning that involves two premises leading to a conclusion. It is a type of deductive reasoning where if the premises are true, the conclusion must also be true. The structure of a syllogism is typically of the form:
- Premise 1: If A, then B.
- Premise 2: If B, then C.
- Conclusion: Therefore, if A, then C.
In the given statement: “If x y and y z, then x z,” we can identify this as a classic example of a syllogism. It involves two conditional statements:
- Premise 1: If x, then y (x → y).
- Premise 2: If y, then z (y → z).
The conclusion drawn from these premises is:
- Conclusion: Therefore, if x, then z (x → z).
This matches the form of a syllogism, where the conclusion logically follows from the premises.
Why the Other Choices are Incorrect:
- A. Contrapositive: The contrapositive of a statement “If A, then B” is “If not B, then not A” (¬B → ¬A). The given statement doesn’t follow this pattern.
- B. Converse: The converse of a statement “If A, then B” is “If B, then A” (B → A). The given statement does not involve swapping the order of the conditions.
- C. Inverse: The inverse of a statement “If A, then B” is “If not A, then not B” (¬A → ¬B). This is not the structure of the given statement either.
Therefore, the statement “If x y and y z, then x z” is best described by the term syllogism, as it follows the logical pattern of reasoning where two premises lead to a conclusion.