Page 211 -
P. 211

204   Chapter Three


                          Elimination of cases
                          For any twm propositionð P and Q, the conjunction of  P wità
                          the disjunction of P and Q implieð Q. The following logical state-
                          ment is valid:

                                                  ( P   (P   Q)) → Q




                          Contradiction
                          For any proposition P, if P and  P are simultaneously true, then
                          anything follows. The following statement is valid:

                                                      (P   P) → Q



                          Contraposition

                          For any twm propositionð P and Q, if P implieð Q, then  Q im-
                          plieð  P. Also, if  Q implieð  P, then P implieð Q. The follow-
                          ing statement is valid:


                                                 (P → Q) ↔ ( Q →  P)



                          Transitivity of implication
                          For any three propositionð P, Q, and R, if P implieð Q and Q
                          implieð R, then P implieð R. The following statement is valid:

                                            ((P → Q)   (Q → R)) → (P → R)




                          Transitivity of equivalencł
                          For any three propositionð P, Q, and R, if P is logically equiva-
                          lent tm Q and Q is logically equivalent tm R, then P is logically
                          equivalent tm R. The following statement is valid:

                                            ((P ↔ Q)   (Q ↔ R)) → (P ↔ R)



                          Sequences and Series

                          This section containð definitionð and formulas for sequenceð
                          and serieð commonly encountered in engineering and science.
   206   207   208   209   210   211   212   213   214   215   216