Which term best describes the statement given below?If a b and b c, then a c.A.Inverse statementB.A syllogismC.Converse statementD.Contrapositive statement

To determine which term best describes the statement "If $a < b$ and $b < c$, then $a < c$", we need to analyze the nature of the statement.

1. Definition of Terms:

   • A. Inverse statement: This refers to a statement formed by negating both the hypothesis and the conclusion of a conditional statement.
   • B. A syllogism: This is a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises).
   • C. Converse statement: This refers to switching the hypothesis and conclusion of a conditional statement.
   • D. Contrapositive statement: This is formed by negating both the hypothesis and conclusion of the converse of a conditional statement.

2. Analysis: The given statement follows a logical form where if one event implies another, then a subsequent implication can also be drawn. This represents a basic property of inequalities in mathematics known as the transitive property, which can be likened to a syllogistic reasoning where a conclusion (that $a < c$) follows from the premises ($a < b$ and $b < c$).

3. Final Answer: Based on the definitions and the analysis above, the correct term that best describes the statement is B. A syllogism.