For a contrapositive statement, what must be done to the two statements?

To form a contrapositive statement, you need to take the original conditional statement, which can be expressed in the form "If P, then Q" (P → Q), and perform two actions: negate both statements and switch their order. This leads to the contrapositive "If not Q, then not P" (¬Q → ¬P).

Negating each statement means that you are saying the opposite of the original statements: if P was true, you state that P is false (¬P), and similarly for Q. Switching the statements involves reversing their order so that the conclusion becomes the premise and vice versa. The importance of the contrapositive lies in its logical equivalence to the original statement; if the contrapositive is true, then the original statement is also true, and vice versa.

This dual process of negating and switching both statements ensures that the new statement accurately reflects the logical relationship inherent in the original. Thus, the correct approach to forming a contrapositive statement is indeed to negate and switch both statements.