In logical terms, what does the contrapositive involve?

In logical terms, what does the contrapositive involve?

• A. Keeping the hypothesis and conclusion the same
• B. Flipping the hypothesis and conclusion
• C. Switching and negating both the hypothesis and conclusion
• D. Creating a new hypothesis

Answer: (C)

The contrapositive of a logical statement involves switching the hypothesis and conclusion and then negating both. For example, if you have a conditional statement "If P, then Q," the contrapositive would be "If not Q, then not P." This transformation maintains the logical equivalence of the original statement; that is, a statement and its contrapositive will always share the same truth value. Understanding the contrapositive is essential, especially in proofs and reasoning, as it allows for alternative perspectives on the relationship between the hypothesis and conclusion while preserving the logical connections inherent in the original statement.

The contrapositive of a logical statement involves switching the hypothesis and conclusion and then negating both. For example, if you have a conditional statement "If P, then Q," the contrapositive would be "If not Q, then not P." This transformation maintains the logical equivalence of the original statement; that is, a statement and its contrapositive will always share the same truth value.

Understanding the contrapositive is essential, especially in proofs and reasoning, as it allows for alternative perspectives on the relationship between the hypothesis and conclusion while preserving the logical connections inherent in the original statement.