What is the definition of a contra-positive in logical reasoning?

What is the definition of a contra-positive in logical reasoning?

• A. Only a positive outcome from premises
• B. A conditional statement derived by negating and interchanging antecedent and consequent
• C. A conclusion drawn from necessary conditions
• D. A statement that fails to follow from a premise

Answer: (B)

The correct answer defines the contrapositive as a conditional statement derived by negating and interchanging the antecedent and the consequent of an original conditional statement. To better understand this, consider a simple conditional statement: "If P, then Q." The contrapositive of this statement would be "If not Q, then not P." This transformation maintains the truth value of the original statement, meaning that if the original statement is true, the contrapositive is also true, and vice versa. This understanding is crucial in logical reasoning because contrapositive reasoning is often employed to validate arguments and assess the validity of deductive reasoning. Recognizing that the contrapositive holds the same truth value as the original statement helps in constructing sound arguments and dissecting complex logical relationships effectively.

The correct answer defines the contrapositive as a conditional statement derived by negating and interchanging the antecedent and the consequent of an original conditional statement.

To better understand this, consider a simple conditional statement: "If P, then Q." The contrapositive of this statement would be "If not Q, then not P." This transformation maintains the truth value of the original statement, meaning that if the original statement is true, the contrapositive is also true, and vice versa.

This understanding is crucial in logical reasoning because contrapositive reasoning is often employed to validate arguments and assess the validity of deductive reasoning. Recognizing that the contrapositive holds the same truth value as the original statement helps in constructing sound arguments and dissecting complex logical relationships effectively.