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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
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