Which term best describes the statement given below?
If a b and b c, then a c.
A. Contrapositive statement
B. A syllogism
C. Inverse statement
D. Converse statement
The Correct Answer and Explanation is :
The correct answer is B. A syllogism.
A syllogism is a form of reasoning in which a conclusion is drawn from two premises, each of which shares a common term with the conclusion. In the given example:
- “If a b” (a is related to b)
- “If b c” (b is related to c)
- Therefore, “a c” (a is related to c)
This reasoning process follows a basic structure of a syllogism, where two premises lead to a conclusion through deductive reasoning.
Explanation:
In logic, a syllogism involves a major premise, a minor premise, and a conclusion. It’s often structured like this:
- Major Premise: All men are mortal.
- Minor Premise: Socrates is a man.
- Conclusion: Therefore, Socrates is mortal.
In this format, both premises lead to a logical conclusion that must be true if the premises are true. In the question, the premises are:
- Premise 1: a is related to b.
- Premise 2: b is related to c.
- Conclusion: Therefore, a is related to c.
This illustrates the transitive property, often used in syllogistic reasoning.
Other Options:
- Contrapositive statement: This involves negating both the hypothesis and conclusion of a conditional statement and then reversing them (If not c, then not a).
- Inverse statement: This involves negating both the hypothesis and conclusion of the original statement without switching them (If not a, then not c).
- Converse statement: This is a statement where the hypothesis and conclusion of the original conditional statement are reversed (If c, then a).
Thus, the given statement is best described as a syllogism because it draws a logical conclusion from two premises.