Philosophy 324 Introduction to Logic I Spring 2017 Midterm Examination This document contains the exam problems. There are 12 problems. Please submit your answers in whatever form you've become comfortable with in your homework and quiz submissions. (For most people, but not for all, this means handwritten and then scanned or photographed and submitted as PDF or JPG files.) Note that in the past, some connectives have not translated well when communicated over D2L. The double-arrow has been the biggest offender, so I've called your attention (in problems 5 and 6) to where I've placed a double-arrow. Part 1 @ 3pts. [Note: in each case you are asked to give a false conclusion. Make sure the falsity of the conclusion is obvious to the reader. \"Portland is above the Arctic Circle\" is obviously false. \"My dog is named Fluffy\" is not obviously false.] 1 Give an example of an English language invalid 3-line argument with a false conclusion. 3 pts. 2 Give an example of a valid English language 3-line argument with a false conclusion. 3 pts. Part 2 @ 5 pts. Using the following interpretations, translate the sentences below into our logical language L1. @ 5 pts. A: Alan goes. B: Betty goes. C: Connie goes. 3 Betty or Alan will go, but Betty will go only if Connie goes. 4 If Alan goes only if Betty goes, then Connie goes. Part 3 @ 10pts. 5 Use a regular truth table to determine whether the following argument is valid. If you obtain answer before filling in all spaces in the field of your table, you may stopbut you must fill in all spaces in your 'reference' columns to the left, and your reference columns MUST BE IN ALPHABETICAL ORDER! (Note: I present the argument in sequent form, and further note that: the connective in the first wff in this sequent is supposed to be a double-arrow, i.e., the first wff is a biconditional.) P Q , ( Q v R) ^ ( R v Q) |= R 6 Use the short method to determine whether the following argument (again presented in sequent form) is valid. If the argument is invalid, give the truthfunctional interpretation that shows this. Note the conclusion is a biconditional. P v Q , (R P) |= Q [ T ( R v S)] 7 Use the short method to determine the 'semantic character' of the following sentence (see p.75 for what I mean by 'semantic character'). [(Q P) ^ (R ^ Q)] (P ^ R) Part 4 @ 10pts. For each of the following sequents, construct a derivation of its conclusion from its premises. (You should be able to do 8 & 9 using 'the first 7 rules' only (though are permitted to use other rules if you so desire.) 8 P ^ Q , (P ^ Q) (R ^ S) , (S v U) W | W 9 P ^ (Q ^ R) , S T , S , (T ^ Q) (U ^ V) | V (Numbers 10 and 11 will require I and/or vE, in addition to 'the first 7 rules'.) 10 P Q , R S | (Q R) (P S) 11 P v (Q ^ R) , (P v Q) S , [S ^ (P ^ R)] T | T (Number 12 will require I.) 12 P Q , Q R , R | (P ^ S)