7.3 Rules Of Replacement I

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Course lecture I developed over section 7.3 of Patrick Hurley\'s "A Concise Introduction to Logic".

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7.3 Rules Of Replacement I

  1. 1. 7.3 Rules of Replacement I
  2. 2. Rules of natural deduction <ul><li>Rule #9 </li></ul><ul><ul><li>DeMorgan’s Rule (DM) </li></ul></ul><ul><ul><ul><li>~(P · Q) becomes (~P v ~Q) </li></ul></ul></ul><ul><ul><ul><li>~(P v Q) becomes (~P · ~Q) </li></ul></ul></ul><ul><li>Rule #10 </li></ul><ul><ul><li>Commutativity (Com) </li></ul></ul><ul><ul><ul><li>(P v Q) becomes (Q v P) </li></ul></ul></ul><ul><ul><ul><li>(P · Q) becomes (Q · P) </li></ul></ul></ul><ul><li>Rule #11 </li></ul><ul><ul><li>Associativity (Assoc) </li></ul></ul><ul><ul><ul><li>P v (Q v R) becomes (P v Q) v R </li></ul></ul></ul><ul><ul><ul><li>P · (Q · R) becomes (P · Q) · R </li></ul></ul></ul>
  3. 3. Rules, continued <ul><li>Rule #12 </li></ul><ul><ul><li>Distribution (Dist) </li></ul></ul><ul><ul><ul><li>P · (Q v R) becomes (P · Q) v (P · R) </li></ul></ul></ul><ul><ul><ul><li>P v (Q · R) becomes (P v Q) · (P v R) </li></ul></ul></ul><ul><li>Rule #13 </li></ul><ul><ul><li>Double negation (DN) </li></ul></ul><ul><ul><ul><li>~~A becomes A </li></ul></ul></ul><ul><ul><ul><li>A becomes ~~A </li></ul></ul></ul>

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