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# MidtermAnswers - 1(20 marks True 07“ false Circle ‘T’...

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Unformatted text preview: 1. (20 marks) ) @ True 07“ false? Circle ‘T’ if the statement is true. Circle ‘F ’ if the statement is false. Assume that go is a WFF of SL. @ F cp may contain exactly 3 symbols. (’6) F All arguments are either valid or unsound. T ® All good arguments are sound arguments. T (F) <p might not be an expression of SL. T @ If (,0 contains exactly 5 symbols then cp contains a two—place connective. The antecedent of “(D —+ (C V D))” is “D”. The scope of “V” in “~(A V B)” is “(A V B)’°\. The word “bank” is not lexically ambiguous. F F T e T (F) Logic is a science which tells us how people actually reason. T (9 There is a valid argument with a hidden assumption and a true conclusion - /20 2. (5 marks) l @ Circle each expression of SL below: «M (((A <—> A) <—> (~B V A» V ~(B (— C») 69 <<C®> [email protected] 3. Make a truth table for each of the following WFFs of SL. (20 marks) a. (B V (B :3 B)) FTFTF :1; Re Do b. (( )H A) ‘ Tl ——l -—| T'Tl ‘4 T)—|‘l‘l——\ T1 TJ—iT‘ ——l-J‘rl—n 2 9 3; ‘T «18? “ﬂ _.|——l~l—-\ l E; __| < 59 7" ‘n-l-—\ lTl‘r‘l 1—) 1-1—1 Dc: 9.. (a: -—I 5?? T 1-3-1 71“?” ”PH-4Q -r\ ﬁ-Hvu-x—wl V T w—J—fﬁ—l I 9’ A A T) 1-! '1‘th 4-4-4 --1 IL'T'T'TI‘TI—l—IA“ \4 —l U: A111 < A-ﬁ—l—l—A-Aq-r‘l ’l T ,1 —-J TJT‘I 2 l—l‘rl‘r 1-1 ~n 4—1-4 4‘47” I TP'H _..| .4 Tlﬁﬂ /m 4. (16 marks) 4 @ Fill in the blanks wzth aA WF F of fSL to make correct, truth tables. a o (A [ﬁt/(- . A] M, tut/17w”; 25W“ 7 Mic/Wag.“ n ‘ VI . , _ 1', _ V” . Y . :{11éfﬁ 51:; ex 1, _. Vii-Mr L: g“ \s /16 5. (12 marks) Suppose that “#” is a new connective edded to SL. Here is the truth table for “((A#B)#A) ” .- I Moo/WM, 12 \$3 cor/M , 6 l , ‘f l , l 0 /12 “5;, WM ' J '6’! Q «M \l ’I for ”,1 Wat/33o G 5*} [AA/«Ck Wore/ﬁne a; furs“ 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 I swim I Will float, but otherwise I’ll be home later. U59“; "‘V' L") ‘ " 0r ”(U—>7”) V (AéSﬁF) -> 2.)) or ((J’->F) V (4[S->F)3l)/ (b) Jason will not meet you, unless you are late. (/‘M V L) (M 9L) (c) Either Jason or Lee ate lunch. (JVL) .(d) Provided that Lee comes, I won’t eat and I won‘t drink. CL 9 (“EX“D)) or ((AEXAD)’> L) (e) If you think I am crazy, then you should go there only if you are not afraid. (e 9 (5', «5 AF)) /10 5| 7. (5 marks) 1 Write down an unsound valid argument with exactly one Premise and where the 5 70735 conclusion 13 different from the premise. -~/ A” 5123 are, (whom/.25 ‘ . 2 I] ; M11\ 2. Explain why your argument is unsound. ‘ ‘ ﬁ/C fit We /} [é/ . >10 t5 .1 / '5 ‘6 /., 8. (12 marks) Assume that each of the following three statements is true: Dil Mil Amy/M a c/M‘for- 1:1 will lam 12mm ‘ If I will not become a doctor, then I Will learn both Russian and Italian. Iwill learn Russian. 2; I L5” [mm MMA Either I will become a doctor and I will learn neither Russian nor Italian, or I will not become a doctor and I will learn both Russian and Italian. 1. Translate each of the three statements into SL, preserving as much structure as possible. Be sure to write down your translation scheme. 61> ‘9 (R ‘51)} R / ((1) 3< (Newly) \/ (AD? (221)» III 7. 7/6) Md?— 2. Will I become a doctor? AtJ P no, ...
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