T F T >F< F T >T< F T T >F< T F >T< F F F >T< T T >T< Truth Table #4 shows that the logic of regular Algebra does distributive property not apply. The truth tables of the two expressions are not equivalent. The final truth tables have been highlighted with arrows. The table {F F F T} is quite different from the table {F T T T}. The functionality of truth tables perhaps has been demonstrated to you. But now you are very curious. Just exactly what happens when you remove the parenthesis? Regular Algebra is no help, the truth tables confirmed that. How about considering if the Expression ~ ( A or B ) is equivalent to ~A and ~B with Truth Table #5. Truth Table #5 A B A or B ~(A or B) ~A ~B ~A and ~B T T T >F< F F >F< T F T >F< F T >F< F T T >F< T F >F< F F F >T< T T >T< Can you believe it? The two expressions are equivalent. This is entirely too weird, but the facts are staring you straight in the face. Perhaps you can appreciate now why this chapter is needed. Armed with only the rudimentary truth tables of the previous section, you would not simply conclude what was just proven. Lack of this knowledge has negative consequences on your programs and it does not help your AP Examination score much either. In Truth Table #6 we take a look at a similar problem that at first may look identical. It is a matter of altering the Boolean operands and checking to see if the expression ~ ( A and B ) is equivalent to ~A or ~B. Truth Table #6 A B A and B ~(A and B) ~A ~B ~A or ~B T T T >F< F F >F< T F F >T< F T >T< F T F >T< T F >T< F F F >T< T T >T<
T F T >F< F T >T< F T T >F< T F >T< F F F >T< T T >T< Truth Table #4 shows that the distributive property logic of regular Algebra does not apply. The truth tables of the two expressions are not equivalent. The final truth tables have been highlighted with arrows. The table {F F F T} is quite different from the table {F T T T}. The functionality of truth tables perhaps has been demonstrated to you. But now you are very curious. Just exactly what happens when you remove the parenthesis? Regular Algebra is no help, the truth tables confirmed that. How about considering if the Expression ~ ( A or B ) is equivalent to ~A and ~B with Truth Table #5. Truth Table #5 A B A or B ~(A or B) ~A ~B ~A and ~B T T T >F< F F >F< T F T >F< F T >F< F T T >F< T F >F< F F F >T< T T >T< Can you believe it? The two expressions are equivalent. This is entirely too weird, but the facts are staring you straight in the face. Perhaps you can appreciate now why this chapter is needed. Armed with only the rudimentary truth tables of the previous section, you would not simply conclude what was just proven. Lack of this knowledge has negative consequences on your programs and it does not help your AP Examination score much either. In Truth Table #6 we take a look at a similar problem that at first may look identical. It is a matter of altering the Boolean operands and checking to see if the expression ~ ( A and B ) is equivalent to ~A or ~B. Truth Table #6 A B A and B ~(A and B) ~A ~B ~A or ~B T T T >F< F F >F< T F F >T< F T >T< F T F >T< T F >T< F F F >T< T T >T<
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