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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»)
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<<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‘
——lJ‘rl—n 2 9
3; ‘T
«18? “ﬂ _.——l~l—\ l
E; __ < 59 7" ‘nl—\
lTl‘r‘l
1—) 11—1 Dc: 9..
(a:
—I 5?? T 131 71“?” ”PH4Q r\ ﬁHvux—wl
V T
w—J—fﬁ—l I 9’
A
A T) 1! '1‘th 444 1 IL'T'T'TI‘TI—l—IA“
\4 —l U: A111
< Aﬁ—l—l—AAqr‘l ’l
T ,1 —J TJT‘I 2 l—l‘rl‘r 11 ~n 4—14 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, _. ViiMr 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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 Spring '08
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