Introdução à Lógica: Proposições e Conectivos

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(\363gico - Joselias@uol.com.br - Prof.: Joselias)Tj
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10 M 
140.59 306.88 m
140.59 204.88 l
178.75 306.88 m
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236.95 306.88 m
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[(a.)-1432(Determine o valor verdade da senten\347a )]TJ
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388.515 733.698 m
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W n
303.796 733.553 m
388.515 733.698 l
388.547 714.978 l
303.828 714.833 l
W n
BT
/F14 1 Tf
10.8 0.018 -0.024 14.16 328.418 720.875 Tm
BX /GS3 gs EX
(\()Tj
ET
Q
q
388.515 733.698 m
388.547 714.978 l
303.828 714.833 l
303.796 733.553 l
W n
303.796 733.553 m
388.515 733.698 l
388.547 714.978 l
303.828 714.833 l
W n
BT
/F14 1 Tf
10.8 0.018 -0.024 14.16 363.457 720.934 Tm
BX /GS3 gs EX
(\))Tj
ET
Q
q
388.515 733.698 m
388.547 714.978 l
303.828 714.833 l
303.796 733.553 l
W n
303.796 733.553 m
388.515 733.698 l
388.547 714.978 l
303.828 714.833 l
W n
BT
/F14 1 Tf
10.56 0.018 -0.029 17.16 305.02 719.849 Tm
BX /GS3 gs EX
([)Tj
ET
Q
q
388.515 733.698 m
388.547 714.978 l
303.828 714.833 l
303.796 733.553 l
W n
303.796 733.553 m
388.515 733.698 l
388.547 714.978 l
303.828 714.833 l
W n
BT
/F14 1 Tf
10.56 0.018 -0.029 17.16 366.699 719.955 Tm
BX /GS3 gs EX
(])Tj
ET
Q
q
303.796 733.553 m
388.515 733.698 l
388.547 714.978 l
303.828 714.833 l
W n
BT
/F15 1 Tf
9.84 0.017 -0.017 9.84 308.736 721.682 Tm
BX /GS3 gs EX
1.595 Tc
[(AB)-220(C)]TJ
ET
Q
q
388.515 733.698 m
388.547 714.978 l
303.828 714.833 l
303.796 733.553 l
W n
303.796 733.553 m
388.515 733.698 l
388.547 714.978 l
303.828 714.833 l
W n
BT
/F14 1 Tf
13.8 0.024 -0.024 13.8 318.216 721.7 Tm
BX /GS3 gs EX
(\331)Tj
ET
Q
q
388.515 733.698 m
388.547 714.978 l
303.828 714.833 l
303.796 733.553 l
W n
303.796 733.553 m
388.515 733.698 l
388.547 714.978 l
303.828 714.833 l
W n
BT
/F14 1 Tf
13.8 0.024 -0.024 13.8 340.536 721.738 Tm
BX /GS3 gs EX
(\336)Tj
ET
Q
q
388.515 733.698 m
388.547 714.978 l
303.828 714.833 l
303.796 733.553 l
W n
303.796 733.553 m
388.515 733.698 l
388.547 714.978 l
303.828 714.833 l
W n
BT
/F14 1 Tf
13.8 0.024 -0.024 13.8 371.735 721.792 Tm
BX /GS3 gs EX
(\333)Tj
ET
Q
BT
/F14 1 Tf
10.8 0 0 14.28 424.27 720.88 Tm
BX /GS3 gs EX
2.378 Tc
(\(\))Tj
10.56 0 0 17.28 389.71 719.775 Tm
6.019 Tc
([])Tj
ET
q
388.51 733.6 72.84 -18.84 re
W n
BT
/F16 1 Tf
9.96 0 0 9.96 393.43 721.72 Tm
-0.001 Tc
0 Tw
( )Tj
/F15 1 Tf
1.108 0 TD
1.579 Tc
[(AB)385(C)]TJ
ET
Q
BT
13.92 0 0 13.92 413.95 721.723 Tm
0.992 Tc
(\331\332)Tj
/F11 1 Tf
13 0 0 13 84.91 702.52 Tm
BX /GS2 gs EX
-0.002 Tc
0 Tw
(Sabendo-se que)Tj
0 -1.634 TD
[(V)129(AL\(A\) = V)118(,)0( V)127(AL\(B\) = F e V)127(AL \(C\) = V)]TJ
/F9 1 Tf
0 -1.837 TD
-0.001 Tc
(Resposta: )Tj
/F14 1 Tf
11.28 0 0 14.04 165.43 657.881 Tm
BX /GS3 gs EX
2.476 Tc
(\(\))Tj
9.24 0 0 17.52 144.55 656.651 Tm
5.706 Tc
([])Tj
11.28 0 0 14.04 246.55 657.881 Tm
2.071 Tc
(\(\))Tj
9.24 0 0 17.52 218.47 656.651 Tm
5.979 Tc
([])Tj
10.8 0 0 19.92 140.59 656.391 Tm
12.364 Tc
({})Tj
/F16 1 Tf
9.96 0 0 9.96 148.15 658.72 Tm
1.369 Tc
[(AB)-109(C)-1873(A)0(B)349(C)-728(F)]TJ
/F14 1 Tf
0.916 0.004 TD
1.421 Tc
[(\331\336)-435(\333)-814(\331)24(\332)-819(=)]TJ
/F11 1 Tf
13 0 0 13 84.91 631.6 Tm
BX /GS2 gs EX
-0.002 Tc
(Obs.:)Tj
/F9 1 Tf
2.298 0 TD
-0.001 Tc
-0.012 Tw
[( Doravante nos exerc\355cios usaremos a nota\347\343o V)128(AL\(X\) para representar o valor)]TJ
-0.12 -1.2 TD
0 Tw
( verdade de X.)Tj
/F11 1 Tf
-4.357 -1.634 TD
-0.002 Tw
[(b.)-1376(Determinar o valor verdade da senten\347a)]TJ
/F14 1 Tf
12.36 0 0 16.32 115.63 567.159 Tm
BX /GS3 gs EX
4.055 Tc
[(\(\))3174(\()1815(\))]TJ
12.24 0 0 19.8 111.91 566.053 Tm
8.52 Tc
([])Tj
/F15 1 Tf
11.4 0 0 11.4 87.19 568.12 Tm
0.006 Tc
0 Tw
[(A)-2156( )10( B)-1514(C)-1661(C)-956(D)]TJ
/F14 1 Tf
0.989 0.003 TD
3.255 Tc
[(\336\333)1760(\331)1805(\332)]TJ
/F11 1 Tf
13 0 0 13 84.91 541.96 Tm
BX /GS2 gs EX
-0.002 Tc
(Sabendo que:)Tj
0 -1.634 TD
[(V)129(AL\(A\) = V)118(,)0( V)127(AL\(B\) = F)90(,)0( V)127(AL\(C\) = F)81(,)0( V)127(AL\(D\) = V)]TJ
/F9 1 Tf
0 -1.929 TD
-0.001 Tc
-0.002 Tw
[(Resposta: V)128(AL )]TJ
/F14 1 Tf
12.36 0 0 16.56 201.55 495.761 Tm
BX /GS3 gs EX
4.055 Tc
[(\(\))3174(\()1825(\))]TJ
12.24 0 0 20.04 197.83 494.656 Tm
8.52 Tc
([])Tj
12.84 0 0 22.08 168.43 494.401 Tm
10.473 Tc
({})Tj
/F16 1 Tf
11.52 0 0 11.52 173.83 496.84 Tm
5.708 Tc
[(AC)4034(C)4763(D)3680(F)]TJ
/F14 1 Tf
0.917 -0.007 TD
3.18 Tc
[(\336\333)1680(\331)1721(\332)1033(=)]TJ
/F16 1 Tf
1.875 0.007 TD0.003 Tc
0 Tw
[( )10( B)]TJ
ET
0.75 w 
BX /GS2 gs EX
126.19 435.7 m
84.91 435.7 l
S
BT
/F11 1 Tf
15 0 0 15 84.91 437.2 Tm
-0.003 Tc
(TAUT)Tj
ET
187.75 435.7 m
126.19 435.7 l
S
BT
15 0 0 15 126.19 437.2 Tm
(OLOGIA)Tj
/F9 1 Tf
13 0 0 13 84.91 403.72 Tm
-0.001 Tc
0.046 Tw
(S\343o mol\351culas que possuem cada uma delas o seu valor verdade sempre verdadeiro)Tj
-2.178 -1.2 TD
-0.003 Tw
(independentemente dos valores l\363gicos das proposi\347\365es \(\341tomos\) que as comp\365em.)Tj
/F8 1 Tf
2.178 -2.4 TD
0.001 Tc
(Exemplo)Tj
/F11 1 Tf
T*
-0.002 Tc
(a.)Tj
/F9 1 Tf
1.089 0 TD
-0.001 Tc
(\(p )Tj
/F14 1 Tf
13.68 0 0 13.68 114.55 324.4 Tm
BX /GS3 gs EX
(\336)Tj
/F9 1 Tf
13 0 0 13 130.39 325.72 Tm
BX /GS2 gs EX
(q\) )Tj
/F14 1 Tf
13.68 0 0 13.68 146.11 324.4 Tm
BX /GS3 gs EX
(\333)Tj
/F9 1 Tf
13 0 0 13 162.43 325.72 Tm
BX /GS2 gs EX
0 Tw
( \()Tj
ET
0.122 0.102 0.09 RG
1 J 1 j 0.84 w 
BX /GS3 gs EX
172.39 325.24 m
172.39 331.84 l
172.75 332.56 l
173.95 332.56 l
174.43 332.32 l
174.79 332.08 l
175.15 331.6 l
175.63 330.4 l
175.63 326.44 l
175.99 325.72 l
176.71 325.48 l
177.91 325.48 l
178.39 326.2 l
178.75 326.92 l
178.75 332.8 l
S
BT
13 0 0 13 181.15 325.72 Tm
BX /GS2 gs EX
-0.002 Tc
( p)Tj
/F14 1 Tf
14.4 0 0 14.4 192.31 324.04 Tm
BX /GS3 gs EX
(\332)Tj
/F9 1 Tf
13 0 0 13 202.75 325.72 Tm
BX /GS2 gs EX
-0.001 Tc
-0.001 Tw
(q\) \351 uma tautologia pois)Tj
-6.905 -2.4 TD
1.632 Tc
-1.633 Tw
[(p q)-334( p)1634( )]TJ
/F14 1 Tf
13.68 0 0 13.68 196.87 293.2 Tm
BX /GS3 gs EX
(\336)Tj
/F9 1 Tf
13 0 0 13 212.71 294.52 Tm
BX /GS2 gs EX
1.448 Tc
-1.449 Tw
[(q \()]TJ
ET
0.6 w 
BX /GS3 gs EX
253.99 293.2 m
253.99 300.04 l
254.23 300.76 l
255.19 300.76 l
255.55 300.52 l
255.79 300.28 l
256.15 299.8 l
256.51 298.6 l
256.51 294.52 l
256.75 293.8 l
257.35 293.56 l
258.31 293.56 l
258.67 294.28 l
258.91 295 l
258.91 301.12 l
S
BT
13 0 0 13 260.83 294.52 Tm
BX /GS2 gs EX
-0.002 Tc
0 Tw
( p)Tj
/F14 1 Tf
14.4 0 0 14.4 272.11 292.84 Tm
BX /GS3 gs EX
(\332)Tj
/F9 1 Tf
13 0 0 13 282.55 294.52 Tm
BX /GS2 gs EX
-0.001 Tc
[(q\))-1090( \(p )]TJ
/F14 1 Tf
13.68 0 0 13.68 332.83 293.2 Tm
BX /GS3 gs EX
(\336)Tj
/F9 1 Tf
13 0 0 13 348.55 294.52 Tm
BX /GS2 gs EX
(q\) )Tj
/F14 1 Tf
13.68 0 0 13.68 364.39 293.2 Tm
BX /GS3 gs EX
(\333)Tj
/F9 1 Tf
13 0 0 13 380.71 294.52 Tm
BX /GS2 gs EX
( \()Tj
ET
0.72 w 
BX /GS3 gs EX
390.19 293.08 m
390.19 300.64 l
390.55 301.48 l
391.51 301.48 l
391.87 301.24 l
392.11 300.88 l
392.47 300.4 l
392.83 298.96 l
392.83 294.4 l
393.19 293.56 l
393.79 293.32 l
394.87 293.32 l
395.23 294.16 l
395.47 295 l
395.47 301.72 l
S
BT
13 0 0 13 397.51 294.52 Tm
BX /GS2 gs EX
-0.002 Tc
( p)Tj
/F14 1 Tf
14.4 0 0 14.4 408.91 292.84 Tm
BX /GS3 gs EX
(\332)Tj
/F9 1 Tf
13 0 0 13 419.35 294.52 Tm
BX /GS2 gs EX
(q\))Tj
-23.566 -1.855 TD
-0.001 Tc
[(V)-1411( V)-2816(V)-3553( V)-5770(V)]TJ
0 -1.412 TD
[(V)-1411( F)-2983(F)-3719( F)-5687(V)]TJ
0 -1.422 TD
[(F)-1577( V)-2816(V)-3553( V)-5770(V)]TJ
T*
[(F)-1577( F)-2983(V)-3553( V)-5770(V)]TJ
ET
0 0 0 RG
0 J 0 j 0.75 w 
207.19 139.54 m
84.91 139.54 l
S
BT
/F11 1 Tf
15 0 0 15 84.91 141.04 Tm
(CONTRADI\307\325ES)Tj
/F9 1 Tf
13 0 0 13 84.91 107.68 Tm
-0.056 Tw
(S\343o mol\351culas que s\343o sempre falsas, independentemente do valor l\363gico das proposi-)Tj
-2.178 -1.2 TD
-0.008 Tw
(\347\365es \(\341tomos\).)Tj
ET
0.122 0.102 0.09 RG
1 J 1 j 0.36 w 
BX /GS3 gs EX
221.35 658.12 m
221.35 659.92 l
221.59 660.88 l
221.71 661.84 l
222.07 662.44 l
222.19 663.16 l
222.67 663.64 l
223.51 663.64 l
223.87 663.4 l
224.11 663.16 l
224.23 662.92 l
224.35 661.96 l
224.59 660.88 l
224.71 659.8 l
224.95 658.84 l
224.95 658.6 l
225.07 658.36 l
225.43 658.12 l
226.39 658.12 l
226.87 658.6 l
227.23 659.32 l
227.59 659.92 l
227.71 660.88 l
227.95 661.84 l
227.95 663.64 l
123.07 565.72 m
123.07 567.88 l
123.55 570.04 l
123.91 570.88 l
124.15 571.72 l
124.75 572.2 l
125.83 572.2 l
126.31 571.96 l
126.43 571.72 l
126.67 571.48 l
126.91 570.4 l
127.15 568.96 l
127.27 567.64 l
127.51 566.56 l
127.51 566.32 l
128.11 565.72 l
129.43 565.72 l
130.03 566.32 l
130.51 567.16 l
130.87 567.88 l
131.35 570.04 l
131.35 572.2 l
208.75 493.48 m
208.75 495.64 l
209.23 497.8 l
209.59 498.64 l
209.83 499.48 l
210.43 499.96 l
211.51 499.96 l
211.87 499.72 l
212.11 499.48 l
212.35 499.12 l
212.47 498.04 l
212.95 495.4 l
213.19 494.2 l
213.19 493.96 l
213.31 493.72 l
213.79 493.48 l
214.99 493.48 l
215.59 493.96 l
216.07 494.8 l
216.43 495.64 l
216.91 497.8 l
216.91 499.96 l
395.11 722.08 m
395.11 723.88 l
395.35 724.72 l
395.47 725.68 l
395.95 726.4 l
396.07 727 l
396.67 727.48 l
397.75 727.48 l
398.11 727.24 l
398.35 727 l
398.47 726.76 l
398.71 725.92 l
398.95 724.72 l
399.07 723.64 l
399.31 722.8 l
399.31 722.56 l
399.55 722.32 l
399.91 722.08 l
401.11 722.08 l
401.71 722.56 l
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402.55 723.88 l
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BT
/F6 1 Tf
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BX /GS3 gs EX
(7)Tj
ET
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BX /GS2 gs EX
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539.01 55.78 l
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BT
/F8 1 Tf
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BX /GS3 gs EX
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(Joselias@uol.com.br - R)Tj
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BX /GS2 gs EX
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BX /GS3 gs EX
(L)Tj
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BX /GS2 gs EX
0 Tc
(\363gico)Tj
ET
0.9 0.9 0.9 rg
BX /GS3 gs EX
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f*
0.48 w 
BX /GS2 gs EX
100.53 383.08 m
288.21 383.08 l
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288.21 362.32 l
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288.21 341.56 l
100.65 320.92 m
288.21 320.92 l
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139.29 403.96 m
139.29 299.2 l
179.25 403.96 m
179.25 299.2 l
225.57 403.96 m
225.57 299.2 l
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BX /GS3 gs EX
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f*
BX /GS2 gs EX
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230.25 683.32 l
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230.25 661.72 l
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1000 M 
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141.69 705.28 m
141.69 640 l
171.69 705.28 m
171.69 640 l
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BT
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0 0 0 rg
0.001 Tc
(Exemplo)Tj
/F11 1 Tf
0 -2.4 TD
-0.002 Tc
[(a.)-344(p)]TJ
/F14 1 Tf
13.68 0 0 13.68 122.13 713.92 Tm
BX /GS3 gs EX
(\333)Tj
ET
0.122 0.102 0.09 RG
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140.37 714.4 m
140.37 721.84 l
140.73 722.68 l
141.69 722.68 l
142.41 722.2 l
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143.01 715.84 l
143.37 715 l
143.97 714.76 l
144.93 714.76 l
145.65 716.44 l
145.65 723.04 l
S
BT
/F11 1 Tf
13 0 0 13 147.57 715.24 Tm
BX /GS2 gs EX
-0.001 Tc
-0.002 Tw
( p \351 uma contradi\347\343o pois)Tj
/F9 1 Tf
-1.578 -1.846 TD
0.571 Tc
-0.572 Tw
[(p )]TJ
ET
0.72 w 
BX /GS3 gs EX
152.73 689.92 m
152.73 697.36 l
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154.05 698.2 l
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155.73 690.4 l
156.33 690.16 l
157.41 690.16 l
157.77 691 l
158.01 691.84 l
158.01 698.44 l
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BT
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BX /GS2 gs EX
0.997 Tc
-0.999 Tw
[( pp)]TJ
/F14 1 Tf
13.68 0 0 13.68 190.89 689.8 Tm
BX /GS3 gs EX
(\333)Tj
ET
0.6 w 
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209.01 697.12 l
209.37 697.96 l
210.33 697.96 l
210.93 697.36 l
211.17 696.88 l
211.53 695.44 l
211.53 691 l
211.89 690.16 l
212.49 689.92 l
213.33 689.92 l
214.05 691.6 l
214.05 698.2 l
S
BT
/F9 1 Tf
13 0 0 13 215.85 691.24 Tm
BX /GS2 gs EX
-0.002 Tc
0 Tw
( p)Tj
-6.831 -1.855 TD
1.42 Tc
[(VF)-1236(F)]TJ
T*
1.586 Tc[(FV)-904(F)]TJ
ET
0 0 0 RG
0 J 0 j 0.75 w 
218.85 590.74 m
99.09 590.74 l
S
BT
/F11 1 Tf
15 0 0 15 99.09 592.24 Tm
-0.001 Tc
(CONTING\312NCIA)Tj
/F9 1 Tf
13 0 0 13 99.09 560.2 Tm
0.087 Tw
(S\343o mol\351culas em que os valores l\363gicos independem dos valores das proposi\347\365es)Tj
-2.188 -1.2 TD
-0.003 Tc
(\(\341tomos\))Tj
ET
146.13 505.42 m
99.09 505.42 l
S
BT
/F11 1 Tf
15 0 0 15 99.09 506.92 Tm
-0.004 Tc
(EQUIV)Tj
ET
279.69 505.42 m
146.13 505.42 l
S
BT
15 0 0 15 146.13 506.92 Tm
-0.002 Tc
0.016 Tw
(AL\312NCIA L\323GICA)Tj
/F9 1 Tf
13 0 0 13 99.09 473.44 Tm
-0.001 Tc
-0.003 Tw
(Duas mol\351culas s\343o equivalentes se elas possuem as mesmas tabelas verdade.)Tj
/F8 1 Tf
0 -2.4 TD
0.001 Tc
(Exemplo)Tj
/F9 1 Tf
0 -2.391 TD
(p)Tj
/F14 1 Tf
13.68 0 0 13.68 107.01 409.72 Tm
BX /GS3 gs EX
(\336)Tj
/F9 1 Tf
13 0 0 13 122.85 411.16 Tm
BX /GS2 gs EX
-0.001 Tc
0 Tw
(q \351 equivalente a )Tj
ET
0.122 0.102 0.09 RG
1 J 1 j 0.48 w 
BX /GS3 gs EX
215.01 411.4 m
215.01 417.76 l
215.25 418.48 l
215.97 418.48 l
216.45 418 l
216.69 417.52 l
216.93 416.32 l
216.93 412.6 l
217.17 411.88 l
217.65 411.64 l
218.37 411.64 l
218.85 413.08 l
218.85 418.72 l
S
BT
13 0 0 13 220.29 411.16 Tm
BX /GS2 gs EX
-0.002 Tc
( p)Tj
/F14 1 Tf
14.4 0 0 14.4 231.69 409.361 Tm
BX /GS3 gs EX
(\332)Tj
/F9 1 Tf
13 0 0 13 242.13 411.16 Tm
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[(Este ar)17(gumento \351 uma fal\341cia, podemos ter as premissas verdadeiras e a conclus\343o falsa.)]TJ
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