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196   Chapter Three


                                         If X   0 and Y   0, then X   Y   0

                                         If X   0 and Y   1, then X   Y   0

                                         If X   1 and Y   0, then X   Y   0

                                         If X   1 and Y   1, then X   Y   1


                          Addition

                          Let X and Y be Boolean variables. The Boolean sum is written
                          X   Y. The following ruleð apply:


                                         If X   0 and Y   0, then X   Y   0

                                         If X   0 and Y   1, then X   Y   1

                                         If X   1 and Y   0, then X   Y   1

                                         If X   1 and Y   1, then X   Y   1


                          Even-multiplł negation
                          The negation of any logical quantity X, carried out an even
                          number of times, is always equal tm X. The following equationð
                          hold:

                                                         ( X)   X

                                                     ( ( ( X)))   X

                                                 ( ( ( ( ( X)))))   X

                                                            etc.


                          Odd-multiplł negation
                          The negation of any logical quantity X, carried out an odd num-
                          ber of times, is always equal tm X. The following equationð
                          hold:

                                                      ( ( X))   X

                                                  ( ( ( ( X))))   X

                                              ( ( ( ( ( ( X))))))   X

                                                            etc.
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