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Unformatted text preview: Problem Set 1 Elementary Logic
Due: 3 October 2007 Student ID Number email Mark “M96
Due 3 October 2007 by 4:00PM.
Submit your problem set to Ms. Loletta Li in Main Building 312. Make sure your problem
set is timestamped. Do not submit assignments by email. Late penalty: 10% for each day late. This problem set will not be accepted after 5 October. Answer the questions on the problem set itself. Write neatly. If the grader cannot read your
handwriting, you will not receive credit. Be sure that all pages of the assignment are securely stapled together.
Check the course bulletin board for announcements about the assignment. Do your own work.
If you copy your problem set, or permit others to copy, you may fail the course. 1. (15 marks) True or fatse? Circle ‘T’ if the statement is true. Circle ‘F’ if the statement ts false. For this question} you should assume that (p is a _WFF of SL. T 513; TF i... If an argument is valid and has a true conclusion, then it is sound.
Some arguments of the form “afﬁrming the consequent” are valid. If to is a negation, then (,0 contains the symbol “)”. An argument is sound if and only if it does not contain a hidden premise. A valid argument with a true conclusion might have a false premise.
Some valid arguments have a false conclusion. Logic describes how people actually reason. The main connective of “N N (NA —> B )” is “—)”. A lexically ambiguous word has more than one meaning in a language. If (p contains exactly 31 symbols then (,0 contains a Oneplace connective. /15 2. (12 marks)
Make a correct truth table for each of the following WFFs of SL. E
1 "‘l <
2
PB
\i
2
8 W~M_.=WHM I ; ‘W‘H ”AnHm ‘ £3
jig
E: 7 ’1'" TRTHpI ,.' ,_, ._ ”a... .m /12 3. (12 marks) Mike following, provide an oppmpm'ote 8L WFF, as speciﬁed. 3,. F111 in the blank with an SL conjunction to make a correct truth table. or” My mm Wad MW
(15%} h 9 ’7 \ d. Fill in the blank with an SL conditional to make a correct truth table. 4. (18 marks) Translate the following statements into SL WFFs, using th
tion scheme. Preserve as much structure as possible. A: Peter is the murderer. B2. Peter knows the victim. C: John knows the victim. D: Paul knows the victim. _
E: Peter has the motive to kill.
F: John has the motive to kill.
G: Paul has the motive to kill. /12 e given transla— a. All that is required for Peter to be the murderer is that he knows the victim. (3%) ar (Me/9:) b. Peter, John and Paul do not all know the victimJ but at least two of them do. (we 24:) w) ttgr are) v (awniv (mi)? c. John does not have d. Not onqﬁcl': @C) ar A(C;? F) e motive to kill even though he {nows the victim. es Paul know the victim, but he also has the motive to kill if Peter is not the murder. (“W (Mag)? W Mia(D 7336?.9 e. Neither Peter "nor John has the motive to kill unless Peter is the murderer. {Airs/F) vs) WWW «F? v Her (e («gt/is) M) f. Peter’s having a motive to kill is both necessary and sufﬁcient fo r his being the murderer, provided that it is false that both John and Paul know the victim. (Mani—>7 (term) /18 5. (17 marks) a. Translate the following statements into SL WFFs, using the given translation
scheme. Preserve as much structure as possible. AzCathy gets an A in her logic course.
B: Cathy gets a B in her logic course.
C: Cathy will be happy. D: Cathy does all the assignments. E: Cathy’s mother will buy Cathy a car. 1. Cathy will be happy if either she gets an A or a B in her logic course. ' (UN/”=95? 2. Cathy gets a B in her logic course if and only if she does all the assignments. (step) 3. It is not true that either Cathy Will not be happy or she does all the assignments. All“ VD) (tr ( (ﬁrth) 4. If Cathy gets an A but not a B in her logic course then her mother will buy her a
new car. C(A%A6)% E) b. Given that all the statements 14 are true, will Cathy’s mother buy her a new car? [half he. " "WW . I /17 6. (5 marks) It is not always appropriate to translate an “H then ...” statement into an SL
W FF using the truthfunctional connective “—>”. Brieﬂy explain why it might not be appropriate to translate the statement “If chickens have lips, then pigs can fly” into
“(C a P)”. (C: Chickensdhage lip 7t M77126 ‘ u‘J/tgilﬂl AW~/ l‘:'
7. (6 marks) in Is “because” a truth~functional connective? Using examples, explain Why or why not.
%W7{ MN. W arm» is aim/51M Mm
was at, Via; a. W We 4: m g .2 team (77x? % W/ /)‘: :57” $3 52M, gaff: ,. 4972a, 8. (15 marks) For each of the following:
Circle “toutology” if it is a WFF of SL that is c tautoiogy.
Circle “contingent” if it is a contingent WFF of SL. Circle “inconsistent” if it is an inconsistent WFF of SL.
Otherwise, don’t circle anything. (UN—Q ~ﬂ)a—> NA) tautology @tgijgﬂexﬁt inconsistent
,esv «Avcwnnewivcn
tefutoi g’y contingent ' inconsistent
g,
,7;ch ((A V O) ——> (A V ~A))
@topéy contingent inconsistent (A H (0' mi ADM?) tautology contingent inconsistent ((N/‘1 H NB)&((~B H £0340 n 0») /M~
tautology contingent infeonsistent) (C H (”353.1% (0’ V A»)
tautOIOgy Eeﬁﬁﬁgeﬁj inconsistent (main) H (NA v ~B)) taumbgy contingent i cziﬁsiste ‘t
W~eww3eon
tautoiogy .7 ﬁpgigingent’" inconsistent ““41 > (B —+ 0)) V ((B + C) —> AD tQ/Lftoiogy contingent inconsistent '
((14 H B) —> “49/:in (14350)»
tautology @tingent inconsistent ...
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