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# midtermans07 - Midterm Test Elementary Logic 13 March 2007...

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Unformatted text preview: Midterm Test Elementary Logic 13 March 2007 Student ID Number Please write clearly. You have 60 minutes to complete this test. Mark —__.__..___I t % 1. (20 marks) 1 P4/@ True or false? Circle ‘T’ if the statement is true. Circle ‘F’ if the statement is false. Assume that (,0 is a WFF of SL. T ® The consequent of “(A —» O)” is “A”. T @ The main connective of “~(A&B)” is “85”. N o argument with a true conclusion contains a hidden assumption. No WFF of SL contains exactly 4 symbols. All arguments are either valid or unsound. If (p contains exactly 5 symbols then go contains a two—place connective. Whenever “(/1853)” is true, “(A —> B)” is also true. Sentential logic is an example of an informal system of logic. T T 6 T (3 T T All good arguments are sound arguments. T F (,0 might not be an expression of SL. / 20 2. (5 marks) / Pi @ Circle each empression of SL below: )) V ~(B *— CD) / 5 1,, mm \Aszl _.|_LIT.1 N TPTF #17: V T! .If T! Tr H T... T? .1! /VI welt, TlTwi @711! 71?. a “I ,1! /I|#II.. letTlTI/IF B Mnk_..|_..|;LlTVr a b. 3‘ Make a truth table for each of the following WFFS of SL. (20 marks) . EJITIIT In) D m, D BTTTrFTTFFN 7r 7 TI! Tr T _.I Owl;le "mewtlhrv TIT/ILLITWTFV T... If TIT Tr: F VT..T.41.1IT.TFCTLLLIFTFikmz /II T if T A .1! T. 1.77.5» Tr 11K ( 3t NFFTTF 7: 1"! TT Tilier TL! fl GIFTFTEITA fr ,7, T: 7:1: Tr mm magma? T E- \$13 MTTTTEELFMT IITILFI..WW\ T T T T K: TF it ti o d. e. /20 4. (16 marks) Fill in the blanks with a. WFF of SL to make correct truth tables. Each WFF you write must contain at least THREE connectives. E - \\ ‘ \v ‘ ’ / 5. (12'markS) Suppose that “#” is a new connective added to SL. Could this be the truth, table for “((A#B)#B) ” .9 Why or why not? w w 6W 1 M ., Pt 7% m Magi-me )- (@MVé). 7m {(memsfxm fa Ae 7/ mm x} M (we? mix ir'WA /12 7mm fez/M2 . If “(Amy )3 F MAM ﬂirt 7 5 5540/ 3 ,1} F, 74% "(f/Jeemg’ Air-J 7‘0 7: u/iw AW /-’1 4mg 5 are F, (yd; r34ﬂa>132 (Jim 74? iii/WA fm7X Zia/é ‘ 6. (10 marks) 2 Translate the following statements into SL, preserving as much structure as possible. Be sure to write down your translation scheme. (a) If Mary heard you she is angry, but otherwise she does not know. Nit/Va"? A£:/V/6lr7 r3 afﬁ/ [Cl/976%?! 10mm . UM?) ,9) v (NM-arujd)) (b) Either Mary or Lee bought a new mobile phone. M: )7“? \$19ny a W Milt/é ﬁlm i _‘ [a 4. W‘ kajlléVJ/ZM. ( M W} (0) Mary will not call you, unless you apologize. Han; C 3 ﬂex); 1177/ CW (701/: . 4’ KM ye/évla V Cieﬁ ea) ar(ﬂCVA) ((21) Provided that Mary does it, I will not do it and I will not let you do it. Hlﬁa/‘ﬂﬂ/wd Dlltriﬂda/Z. Allmﬁﬂywﬂwz. (M§(Apsnu) (e) If you think I am crazy, then you should go there only if you are not afraid. 5: ts. star .2 aa% CAazy. é} : 7m I‘anel its 710% - F " rm él/Le . (c ~> (d7 413)) m 6 7. (5 marks) 1. Write down a. saund argument with exactly one premise, and where the conclusion is different from the premise. ZH/ 7’2 r_- ' :..,' ‘__,._, IMAM 7p, (Me/Let In, Mr re 04 mir- H‘i p2. . 2. Explain why your argument is sound. 8. (12 marks) Assume that each of the following four statements is false: Gerald is not friendly. If Herman was not in Las Vegas that day, then Herman and Lola are both liars. Either Herman was in Las Vegas that day and Herman is a liar, 0r Herman was not in Las Vegas that day and Lola. is not a liar. Gerald is friendly only if Lola is not a liar. 1. Tt'anslate each of the three statements into SL, preserving as much structure as possible. Be sure to write down our translation scheme. - y F > 6M1 a M ’W‘ V? ﬂamers UM A law I/ﬁea Zia/4&7 - H-‘f/MMM 1:4 61 “ZAM- “VéWmD tales ass/L W twee J65“ My! Q ull- .. 2. Was Herman in Las Vegas that day? Nan Em ‘ ‘ 7 /12 ...
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