R——>~T

　　~R

　　Therefore， T

　　[Note： Two negatives make a positive， so the conclusion ~（~T） was reduced to

　　T.] This diagram clearly shows that the argument is committing the fallacy

　　of denying the premise. An if-then statement is made； its premise is negated

　　； then its conclusion is negated.

　　Transitive Property

　　A——>B

　　B——>C

　　Therefore， A——>C

　　These arguments are rarely difficult， provided you step back and take a bir

　　d's-eye view. It may be helpful to view this structure as an inequality in m

　　athematics. For example， 5 > 4 and 4 > 3， so 5 > 3.

　　Notice that the conclusion in the transitive property is also an if-then sta

　　tement. So we don't know that C is true unless we know that A is true. Howev

　　er， if we add the premise “A is true” to the diagram， then we can conclude t

　　hat C is true：

　　A——>B

　　B——>C

　　A

　　Therefore， C

　　As you may have anticipated， the contrapositive can be generalized to the tr

　　ansitive property：

　　A——>B

　　B——>C

　　~C

　　Therefore， ~A

　　Example： （Transitive Property）

　　If you work hard， you will be successful in America. If you are successful i

　　n America， you can lead a life of leisure. So if you work hard in America， y

　　ou can live a life of leisure.