Contrapositive Arguments - Important

The contrapositive of a conditional statement is formed bynegating both the hypothesis and the conclusion, and then interchangingthe resulting negations.
In other words, the contrapositive negates and switches the parts of the sentence. It does BOTH the jobs of the INVERSE and the CONVERSE.

Example:

Conditional: "If 9 is an odd number, then 9 is divisible by 2." (true) (false)
Contrapositive: "If 9 is not divisible by 2, then 9 is not an odd number." (true) (false) An important fact to remember about the contrapositive, is that it always has the SAME truth value as the original conditional statement. **If the original statement is TRUE, the contrapositive is TRUE. If the original statement is FALSE, the contrapositive is FALSE. They are said to be logically equivalent. Conditional Contrapositive Source: http://regentsprep.org/regents/math/relcond/Lcontrap.htm Example: If A, then B. If B, then C. If C, then D. If all of the statements above are true, which of the following must also be true? (A) If D, then A. (B) If not B, then not C. (C) If not D, then not A. (D) If D, then E.（C） (E) If not A, then not D. Ans: C