[npl] / trunk / NationalProblemLibrary / SUNYSB / contradiction.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

Revision 322 Revision 323
38 row( 'd', 'Commutative Properties '), 38 row( 'd', 'Commutative Properties '),
39 row( 'e', 'Associative Properties '), 39 row( 'e', 'Associative Properties '),
40 row( 'f', 'Distributive Properties '), 40 row( 'f', 'Distributive Properties '),
41 row( 'g', 'Equivalence of Contrapositive '), 41 row( 'g', 'Equivalence of Contrapositive '),
42 row( 'h', 'Definition of Implication '), 42 row( 'h', 'Definition of Implication '),
43 row( 'i', 'Definition of Equivalence '), 43 row( 'i', 'Definition of Equivalence '));
44BEGIN_TEXT
44 row( 'j', 'Identity Laws $$(p \vee F = p \wedge T = p)$$ '), 45 \{ row( 'j', 'Identity Laws $$(p \vee F = p \wedge T = p)$$ ')\}
45 row( 'k', 'Tautology $$(p \vee \neg p = T)$$ '), 46 \{ row( 'k', 'Tautology $$(p \vee \neg p = T)$$ ') \}
46 row( 'l', 'Contradiction $$(p \wedge \neg p = F)$$ '), 47 \{ row( 'l', 'Contradiction $$(p \wedge \neg p = F)$$ ') \}
48END_TEXT
49TEXT(
47 row( 'm', 'Negation of the goal to prove '), 50 row( 'm', 'Negation of the goal to prove '),
48 row( 'n', 'Modus Ponens'), 51 row( 'n', 'Modus Ponens'),
49 row( 'o', 'Modus Tollens'), 52 row( 'o', 'Modus Tollens'),
50 row( 'p', 'Transitivity of Implication'), 53 row( 'p', 'Transitivity of Implication'),
51 row( 'q', 'Conjunctive Simplification'), 54 row( 'q', 'Conjunctive Simplification'),
61BEGIN_TEXT 64BEGIN_TEXT
62 $PAR 65$PAR
63 We want to prove $$s$$ by a proof by contradiction from the following propositions. 66 We want to prove $$s$$ by a proof by contradiction from the following propositions.
64END_TEXT 67END_TEXT
65 68
66TEXT( 69TEXT( begintable(1));
67 begintable(1), 70BEGIN_TEXT
68 row( '$$p \rightarrow q$$' ), 71 \{ row( '$$p \rightarrow q$$' ) \}
69 row( '$$r \rightarrow q$$' ), 72 \{ row( '$$r \rightarrow q$$' ) \}
70 row( '$$\neg q$$' ), 73 \{ row( '$$\neg q$$' ) \}
71 row( '$$\neg(s \wedge T) \rightarrow p$$' ), 74 \{ row( '$$\neg(s \wedge T) \rightarrow p$$' ) \}
72 endtable() 75END_TEXT
73); 76TEXT( endtable() );
74 77
75BEGIN_TEXT 78BEGIN_TEXT
76 $PAR 79$PAR
77 $$\neg s$$ by \{ ans_rule(1) \} 80 $$\neg s$$ by \{ ans_rule(1) \}
78END_TEXT 81END_TEXT
104elsif ($version == 2) 107elsif ($version == 2)
105{ 108{
106BEGIN_TEXT 109BEGIN_TEXT
107 $PAR 110$PAR
108 We want to prove $$d$$ by a proof by contradiction from the following propositions. 111 We want to prove $$d$$ by a proof by contradiction from the following propositions.
109END_TEXT
110 112
111TEXT(
112 begintable(1), 113\{ begintable(1) \}
113 row( '$$a \rightarrow b$$' ), 114\{ row( '$$a \rightarrow b$$' ) \}
114 row( '$$r \rightarrow b$$' ), 115\{ row( '$$r \rightarrow b$$' ) \}
115 row( '$$\neg b$$' ), 116\{ row( '$$\neg b$$' ) \}
116 row( '$$\neg(d \wedge T) \rightarrow a$$' ), 117\{ row( '$$\neg(d \wedge T) \rightarrow a$$' ) \}
117 endtable() 118\{ endtable() \}
118);
119 119
120BEGIN_TEXT
121 $PAR 120$PAR
122 $$\neg d$$ by \{ ans_rule(1) \} 121 $$\neg d$$ by \{ ans_rule(1) \}
123END_TEXT 122END_TEXT
124ANS(str_cmp("m")); 123ANS(str_cmp("m"));
125 124
149else 148else
150{ 149{
151BEGIN_TEXT 150BEGIN_TEXT
152 $PAR 151$PAR
153 We want to prove $$s$$ by a proof by contradiction from the following propositions. 152 We want to prove $$s$$ by a proof by contradiction from the following propositions.
154END_TEXT
155 153
156TEXT(
157 begintable(1), 154\{ begintable(1) \}
158 row( '$$p \rightarrow b$$' ), 155\{ row( '$$p \rightarrow b$$' ) \}
159 row( '$$r \rightarrow b$$' ), 156\{ row( '$$r \rightarrow b$$' ) \}
160 row( '$$\neg b$$' ), 157\{ row( '$$\neg b$$' ) \}
161 row( '$$\neg(s \wedge T) \rightarrow p$$' ), 158\{ row( '$$\neg(s \wedge T) \rightarrow p$$' ) \}
162 endtable() 159\{ endtable() \}
163);
164 160
165BEGIN_TEXT
166 $PAR 161$PAR
167 $$\neg s$$ by \{ ans_rule(1) \} 162 $$\neg s$$ by \{ ans_rule(1) \}
168END_TEXT 163END_TEXT
169ANS(str_cmp("m")); 164ANS(str_cmp("m"));
170 165

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