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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 |
