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:
Correct Answer: B. A syllogism
Explanation
The statement “If a → b and b → c, then a → c” is best described as a syllogism.
A syllogism is a form of deductive reasoning in logic, where a conclusion is drawn from two given or assumed premises. The classic structure of a syllogism is:
- Premise 1: If a, then b.
- Premise 2: If b, then c.
- Conclusion: Therefore, if a, then c.
This pattern is valid in logic and is often referred to as hypothetical syllogism or transitivity of implication. It’s a way of combining two conditional (if-then) statements to infer a new one.
Why Not the Other Options?
- A. Contrapositive statement
A contrapositive of a conditional statement if p, then q is if not q, then not p. This changes both the hypothesis and conclusion to their opposites and switches them. It is logically equivalent to the original statement, but it’s not what’s being described here. - C. Inverse statement
The inverse of if p, then q is if not p, then not q. Like the contrapositive, it alters the original statement, but unlike the contrapositive, it is not logically equivalent. - D. Converse statement
The converse of if p, then q is if q, then p. Again, this switches the direction of implication, but the original statement is describing a chain of reasoning, not a reversal.
Conclusion:
The reasoning used in “If a → b and b → c, then a → c” is a textbook example of a syllogism, specifically a hypothetical syllogism. It reflects the logical structure that allows conclusions to be drawn from multiple premises in a step-by-step manner.
