GMT考试--Testprep数学精解（3）

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. 　　LET W STAND FOR "YOU WORK HARD," S STAND FOR "YOU WILL BE SUCCESSFUL IN AMER 　　ICA," AND L STAND FOR "YOU CAN LEAD A LIFE OF LEISURE." NOW THE FIRST SENTEN 　　CE TRANSLATES AS W-->S, THE SECOND SENTENCE AS S-->L, AND THE CONCLUSION AS 　　W-->L. COMBINING THESE SYMBOL STATEMENTS YIELDS THE FOLLOWING DIAGRAM: 　　W-->S 　　S-->L 　　THEREFORE, W-->L 　　THE DIAGRAM CLEARLY DISPLAYS THE TRANSITIVE PROPERTY. 　　DEMORGAN’S LAWS 　　~(A & B) = ~A OR ~B 　　~(A OR B) = ~A & ~B