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2 be logical
INTERMEDIATE logic Lessons 16-19
| Question | Answer |
|---|---|
| rules of replacement | forms of equivalent statements |
| The rules of replacement work in _________ directions across the equal sign. | both |
| The rules of _____________________ ALLOW one proposition to REPLACE an equivalent proposition, even in the middle of a longer compound proposition. | REPLACEMENT |
| The rules of _____________________ do NOT allow one proposition to replace an equivalent proposition. | INFERENCE |
| Sometimes it helps to work a proof | backwards or to simultaneously work forward from the premises AND backward from the conclusion, trying to get them to match somewhere in the middle. |
| When solving a proof, FIRST look at the CONCLUSION and ask: | "How can I get that conclusion from those premises?" |
| If a conditional is in the conclusion, you will most likely need to use either | Hypothetical Syllogism -or- Material Implication. |
| To get a CONDITIONAL from a DISJUNCTION, use | Material Implication. |
| The only rule that DROPS a constant is | Simplification. But you CANNOT simplify within a proposition. |
| Sometimes you must think of an entire proposition or multiple components of the proposition as | p or q. |
| If the CONCLUSION is in the form of "p and q," use | CONJUNCTION, deducing both conjuncts from the premises. |
| If the CONCLUSION is in the form of "p v q," either deduce one of the disjuncts from the premises and use Add. to get the other -OR- | use DeM, CD, or Impl., all of which have disjunctions as conclusions. |
| If a constant is in the conclusion that is not in the premises, use | ADDITION somewhere in the proof to add that new constant. |
| There are usually | many ways to solve a proof. |
| Rules of Inference are forms of | valid arguments. |
| conditional proof | a special rule in a formal proof which allows us to assume the antecedent of the conditional and, once we deduce the consequent, to conclude the entire conditional |
| IF assuming the antecedent of a conditional allows us to conclude the consequent, THEN | we can conclude the entire conditional. This is why CPA are valid. |
| You may NOT select one step of a Conditional Proof Assumption to use | later in the proof. |
| Conditional Proof Assumptions may ONLY be made when using | the Conditional Proof. |
| When using any part of the conditional proof, you must use | ALL of the Conditional Proof. |
| Reductio Ad Absurdum | a special rule that allows us to ASSUME the negative of a proposition, DEDUCE a self-contradiction, then CONCLUDE the entire proposition |
| Latin for "bringing to absurdity" | reductio ad absurdum |
| If the negation of a proposition leads to a contradiction of the form "p AND not p," then we may | conclude the original proposion. |
Created by:
MrsHough
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