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Tue Aug 8 15:08:53 2006 UTC (6 years, 9 months ago) by jjholt
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Added tags.  --JH


    1 ## DESCRIPTION
2 ## Discrete Mathematics
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('discrete mathematics','logic','proof')
6 ## Tagged by cmd6a 8/6/06
7
8 ## DBsubject('Discrete Mathematics')
9 ## DBchapter('Logic')
10 ## DBsection('First Order Logic')
11 ## Date('')
12 ## Author('')
13 ## Institution('SUNYSB')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();
22            'PGbasicmacros.pl',
23            'PGchoicemacros.pl',
25 );
26 TEXT(beginproblem());
27 $showPartialCorrectAnswers = 0; 28 29 BEGIN_TEXT 30 For the following proof (of equivalence of 2 formulae) provide the justifications at each step, 31 using the following equivalences. Use the following key: 32$PAR
33 END_TEXT
34 TEXT(
35     begintable(2),
36          row( 'a', 'Idempotent Law'),
37          row( 'b', 'Double Negation'),
38          row( 'c', 'De Morgan~~'s Law'),
39    row( 'd', 'Commutative Properties '),
40          row( 'e', 'Associative Properties '),
41          row( 'f', 'Distributive Properties '),
42          row( 'g', 'Equivalence of Contrapositive '),
43          row( 'h', 'Definition of Implication '),
44          row( 'i', 'Definition of Equivalence '),
45          row( 'j', 'Identity Laws $$(p \vee F \equiv p \wedge T \equiv p)$$ '),
46          row( 'k', 'Tautology $$(p \vee \neg p \equiv T)$$ '),
47          row( 'l', 'Contradiction $$(p \wedge \neg p \equiv F)$$ '),
48     endtable()
49 );
50
51 # Christelle+proof proofReason3.pg
52
53 $version = random(1,2,1); 54 if ($version == 1)
55 {
56
57 BEGIN_TEXT
58     $PAR 59 $$p \rightarrow (p \wedge q)$$ $$\equiv$$$BR
60     $$\neg p \vee (p \wedge q)$$ by  \{ ans_rule(1) \}
61 END_TEXT
62 ANS(str_cmp("h"));
63
64 BEGIN_TEXT
65     $$\equiv$$ $$(\neg p \vee p) \wedge (\neg p \vee q)$$
66     by \{ ans_rule(1) \}
67 END_TEXT
68 ANS(str_cmp("f"));
69
70 BEGIN_TEXT
71     $$\equiv$$ $$(p \vee \neg p) \wedge (\neg p \vee q)$$
72     by \{ ans_rule(1) \}
73 END_TEXT
74 ANS(str_cmp("d"));
75
76 BEGIN_TEXT
77     $$\equiv$$ $$T \wedge (\neg p \vee q)$$
78     by \{ ans_rule(1) \}
79 END_TEXT
80 ANS(str_cmp("k"));
81
82 BEGIN_TEXT
83     $$\equiv$$ $$(\neg p \vee q) \wedge T$$     by \{ ans_rule(1) \}
84 END_TEXT
85 ANS(str_cmp("d"));
86
87 BEGIN_TEXT
88     $$\equiv$$ $$\neg p \vee q$$ by \{ ans_rule(1) \}
89 END_TEXT
90 ANS(str_cmp("j"));
91 }
92 else
93 {
94 BEGIN_TEXT
95     $PAR 96 $$\neg(\neg p \wedge q) \wedge (p \vee q)$$$BR
97     = $$(\neg(\neg p)\vee \neg q)\wedge( p \vee q)$$ by \{ ans_rule(1) \}
98 END_TEXT
99 ANS(str_cmp("c"));
100
101 BEGIN_TEXT
102     = $$(p \vee \neg q) \wedge (p \vee q)$$ by \{ ans_rule(1) \}
103 END_TEXT
104 ANS(str_cmp("b"));
105
106 BEGIN_TEXT
107     = $$p \vee (\neg q \wedge q)$$ by \{ ans_rule(1) \}
108 END_TEXT
109 ANS(str_cmp("f"));
110
111 BEGIN_TEXT
112     = $$p \vee (q \wedge \neg q)$$ by \{ ans_rule(1) \}
113 END_TEXT
114 ANS(str_cmp("d"));
115
116 BEGIN_TEXT
117     = $$p \vee F$$ by \{ ans_rule(1) \}
118 END_TEXT
119 ANS(str_cmp("l"));
120
121 BEGIN_TEXT
122     = $$p$$ by \{ ans_rule(1) \}
123 END_TEXT
124 ANS(str_cmp("j"));
125 }
126
127 ENDDOCUMENT();
128
129
130