Tips+Exam+2

# Tips+Exam+2 - Tips Refer to the review notes to see how to...

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Tips: Refer to the review notes to see how to do the various types of derivations and strategies. Follow these steps once you’ve written the problem out (i.e. once you’ve put the premises on separate lines and announced that you are going to show the conclusion). You will need to repeat some or all of steps 1-3 if you generate new showlines as you proceed. (1) Look at the formula that you have to show. Is it a conditional formula (main connective is an arrow)? YES- Do CONDITIONAL DERIVATION [follow tips again from beginning to determine how to show the consequent]. NO – Go to (2) (2) Scan the available lines and the formula you need to show. Can you straightforwardly see that a direct derivation will work? YES – Do DIRECT DERIVATION NO – Go to (3) (3) What type of formula do you need to show? (a) A negation (main connective is a tilde) - Do INDIRECT DERIVATION [type 1] (b) A disjunction (main connective is a wedge) – FOLLOW THE SHOW DISJUNCTIVE STRATEGY. (c) A conjunction (main connective is an ampersand) – FOLLOW THE SHOW CONJUNCTION STRATEGY (d) A biconditional (main connective is a double-arrow) – FOLLOW THE BICONDITIONAL STRATEGY. (e) A single letter – Do INDIRECT DERIVATION [type 2]. . After you’ve set up the appropriate derivation, go to step 4 (4) Next, try to see what steps you can take given the premises and any assumptions that you have. Here are some tips of how to proceed if you get stuck seeing what steps can be done. (a) If you have a premise or assumption that is a conditional then you should check to see if you can do an arrow-out (now or soon). You should see if you have (or can get) on its own line either (a) the formula that is the antecedent of the conditional, or (b) the negation of the formula that is the consequent of the conditional. E.g. suppose you have P Q as a premise or assumption. Then you should be looking if you have already or can easily get either (a) P or (b) ~Q.

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(b) If you have a premise or assumption that is a disjunction then you should check to see if you can do a wedge-out (now or soon). You should see if you have (or can get) on its own line either the formula that is the negation of one of the disjuncts. E.g. suppose you have P v Q as a premise or assumption. Then you should be looking if you have already or can easily get either (a) ~P, or (b) ~Q. (c) If you have a premise or assumption that is a biconditional then do double-arrow out. This will give you two conditional statements (on separate lines of course) and now you can ask whether you can do arrow-out (see 4a). Notice that it is likely you will only need to use one of the conditional formulas you can derive from the biconditional. If you can immediately see which one of these you will need then you don’t need to bother write out the one that will be redundant.
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