5000 Exercicios de LAC - FBF, Tableau Semântico

Prévia do material em texto

Para cada uma das fórmulas abaixo,
a) verifique se é fbf
b) ponha os parênteses para melhorar a legibilidade
c) construa o tebleau semântico para V e para F
A<->~C^C^~A
A->C->B
~C->~C<->~B->~C<->~B
AvAv~B<->A<->~B
B<->~Bv~A^~B
BvB<->~C<->C<->~B
~A->~CvB
C->~Bv~B->~A
~Cv~C
AvB<->~C
~A^~C^C->A^~B
~A^C
~B^~A
C<->B
AvB^~CvA->~A<->C
A<->CvC
Av~BvA^~B->~B^~A<->C
~AvC^A
C<->~A->CvAvC
~B^BvC<->A
CvB<->~C^C^~B->A^~B
~AvC
B^~C^B<->C
C->~C^~A
~C<->A<->Bv~A
~C^~C^A->A
~B<->C<->B
BvC->C->~AvB
~BvA^C<->~A^B
~A<->Av~B^~CvA
Av~C->A->B
~B->~C^~A->~C
C^C^~B<->A->B
C^~A
~B<->~B<->~A->C
C^AvAvA->~A
A->C->~B
A<->B
AvA->~C->A<->C^A^B
C->A->~B
~AvAv~Cv~A<->C^B
A->B<->~C^~A<->~B<->A<->~B
~B^~B<->A
~Av~C^~Av~B
B->~B^~A^A->A^~A
~B^~Bv~Cv~C^A
B->B->~C^B
Bv~B<->~A->~B^~B->Cv~A
C^~B
C<->AvC->~AvC
C<->B^A
~B<->Cv~A<->~Av~C<->B
~AvB->~B
B^A<->B
~A->~C->A^C
A^~C->CvB^AvA
~CvA->~A->C<->Bv~BvB
AvB->~B
BvA^~C->B
A^~C->~A^A->~C<->~B<->A
~CvA<->Av~C<->~B^C->~B
B->~C^~A->B
C^~A<->~A^~A->~Av~B
A^B
~B<->~B
C<->~A
C->~C
C->~C<->C
~A<->A
~A<->A^A<->~C
B^~AvA->C->C
A->C
A^~C^B
~A->~B->C<->C
~A^~B
~Bv~B<->~C->B<->~B
C<->~C->~A
~Bv~B<->Cv~C<->~C
~B->~A^~B<->B^C<->~B
CvA^C->~A
~C->C
A<->B<->A->C->~A
~CvA
~CvC<->~B<->~C^~Cv~A^B
~C^BvB<->Av~C
~A^~BvC<->C^~A
~Bv~B
Av~BvC^B->B->~C
~B^~C->C<->~Bv~A->~C<->B
~Bv~C->~C
A<->B^~A^~CvC
Bv~B->C->~A<->C^~B
CvA^Av~B^AvAv~C
B->~B
Av~CvC->~B->~C<->B
A->B
~A->~B
C^~C<->~C<->A
~A->~A^B<->C^~AvB<->B
~C<->~C->~A<->~A<->~B
B<->A<->~C^A->~C<->BvA
A^~BvBv~A->A
C->B->Bv~C
C<->~C->~A^~C->C->~A
~C->C<->~C^~C
A^CvB->~C^A
A<->B^~B<->~B^~A
A^B->C
~Av~A<->C->A^~A->~A
~C->B^~A<->C^~A
C->~Cv~C<->BvC<->A->A
~Cv~A<->A
~A->C^~A
BvCvB<->BvB^A
~B<->A->~A^~A->~C<->~B->C
~B->B<->~Bv~A
~B<->~C<->A->~A^~Av~B<->~A
~C<->A<->~BvB<->A
B<->A^CvA
~B^~C^~CvB^~B
~C^~Av~A
B<->~A<->A^~C->C<->C->C
A->~C
Cv~Cv~B->CvA
~B^~A^C<->~A<->A^~A^~B
Cv~Bv~AvA^~C
~B^~BvC<->Av~A
B->B->C^~A->~A^~Bv~B
A->~C^C<->~B<->~C
B->~A<->C
~C->C^~A
C<->~B
AvB<->~A->~A^B
~Av~B->~B
~B<->A
~A<->B
~A->C
A->C^~B^AvC
~AvC^A^~C^~Cv~B
Bv~Cv~A<->A
~A^~C<->B^AvA<->B
~B->B
C->A^~C<->~A
~B->C
~C<->~A->B
~B^AvC
C->~A^A^~B->C^C<->~C
~Av~Cv~B^~Av~C^~A
~C^A
~AvB->~B->~Bv~Cv~B
B->B
B<->A^A^~C^~B<->~A^~A
~C<->Bv~A->~A->~A->B->C
~C^AvC<->BvB
C^~A<->~A
~B->BvA->B^Bv~A
~C->Bv~C^~Av~B^AvB
B^~C->BvC<->~C<->Cv~B
BvA<->~A->A
B^~B<->~A^C
~C^~A^A
~A<->~Bv~Bv~A<->~C
~Cv~C->~A
~A->A->~B->~B->B->~C
AvB
~B->~B^B
~B^~C
~A<->~Bv~AvB
~Bv~C<->C<->~Av~A->B
~B^~A<->B->Bv~C^~Cv~B
B^~B<->AvC->C^B
Av~Av~A<->~Av~B^C
CvCv~B->~C
~Bv~AvA<->~CvB<->~C
Av~A
~B<->B->C
~A->B^~B<->~C->C
C->C<->B->~B->B
A^AvBvA<->~Cv~A
~C<->~Bv~B<->A^~C
A<->B^~C^A->~B->~B^A
~BvC<->A->~A->C
C<->~A->~AvCv~C->~C
~Bv~B^~Bv~B^~B
Cv~Cv~A
CvA<->~A
~B<->~C<->~C
B^Cv~A^A->C
~Av~A^Bv~C
~B->A^A<->~A<->B
Bv~A<->Bv~A->~A->~C
~B<->~C^A->B
~B->A^C^A
~B<->~Bv~B^B^B->A
~AvB<->~C^~A
~A->~Av~C->~AvC^C->~A
~C^~A->~B<->~B->~B<->~A<->~A
B->C<->B<->~C->A^~A
C->C
~C<->A<->B
B->C->~AvA<->~Bv~C
~B^~A->~C^C<->~A->~C->~B
AvC->~A->C
Cv~A->C->~AvB->~A->B
~B<->~B<->~B^~A
C->Bv~B<->A<->~A
~C^~A
~C^A->C^~AvAvCvB
~B->B->B^B
~Av~C^B^Av~B
~B^~C^B^AvAv~C^~C
A<->~Bv~C->~Bv~C
B<->C->~A->C
B^~C<->~C
A^C->~C<->~C->~AvC
A^~C<->AvBvB<->Cv~C
BvB^~B
~B->C<->CvA->~C
~B->B^~B<->~C
~C^C<->~A
C^~A<->A^~B->AvB^~C
Bv~B->C->B
B<->A->~A<->B
C->C<->B->C^~B<->A->~A
~A^~B^~Cv~A->C<->C
~C<->CvBv~A
~A^BvC->B<->C->A
A<->A^B
~C<->Cv~C<->C<->~A<->C^B
CvB
~A^C<->A<->~A
B<->~C^~A
C->~Av~Cv~B^~A->B
~B->Cv~AvAvA
~BvCvCvB^~B
~B^C^CvC
BvA^~A->B
~CvC<->~B
~B<->~C->A<->~CvB
C<->~BvB->AvA
CvC
C^B^C->A
~B^~B
~B<->B->A<->A
B^Av~A^~A
B^~B<->C<->CvC
A->~C^Av~B^~C
~C<->Cv~B<->~B<->~A
C^A^B^A^C<->~B->A
A^~Bv~AvA
B<->C<->B
~B<->~C
A->AvC
~C->~Av~B
~CvA->C->~B->B<->C<->A
B<->~CvB
B^C^C^BvA^~C
~C^~A^~C^~B<->~B
~A<->~C->A<->Bv~C
~C->B
~A<->CvCvB^C->~C
CvB^~A->C->~C<->B<->A
A<->~B
~Bv~A^~A->C<->B
~B<->B
A^B->B^C^~Cv~A
C<->Cv~C
BvAvB->~A->C
~C<->Cv~C<->C->~C
B^~A^B
~B<->~Bv~A
Bv~A<->A->~A<->B^~B
~A->~B^A<->C
A<->~Av~A^BvCvC^~B
~B^B^C^~A->A<->Av~A
~A^Bv~C
~C->~C^A->B<->B
~B->C<->~A^~AvB
C->~CvB->AvB->A
B^BvA<->~AvC^C<->C
~A->~B->Bv~A
A<->C^C->~A->B<->~B
C^~A^~C->~B->~CvB
BvCv~A<->~B^B^~A
~A<->B->B<->~Cv~A
A^~C->~Av~A
~B^Av~C->~B
B^A<->A<->~B<->~A^C
A^B->~B^~A<->C^~A
A<->~C
~AvA
~Cv~B^B^~A
B->Av~Bv~A->~C^B->A
Cv~C^~C
A<->~CvB
~B^C->C
A<->~CvB->~C
Bv~B<->C^B
B<->A<->~C->C<->A^C
B^C->~A
CvBvBv~B<->B->B<->~B
~B<->C<->~A<->~B
B^~B->~B
~CvAv~C
~B->C^~A->BvCv~A
~B<->A<->A<->~CvB<->~C
AvC->~C->~B
~B^C<->~C->~Av~C<->A^A
~CvAvB
B^~C<->~B^~Av~C^B^C
CvC->~A<->B
~B->Av~C<->A
~Cv~B<->~A->~A^B
~B^~B<->~B->~A
C->~A<->~AvC<->~C^B<->A
A^~B
B->C^~Bv~B^BvCv~C
~C<->A^~B
~C^C
A->~C<->~C->C
~B<->C->~CvBv~B
~A<->~C->C<->~Cv~A
~B<->~C^~C->BvB^C
~CvB<->~B->Av~A
C->~C->A^B^~C
~B->~B<->~A->~CvC
B^C
~AvCvB
B<->C->B
~BvB^~A->~B<->B<->~B
C->A<->~Cv~CvA->B
C^C^~Bv~A<->C->~B
~A<->C<->B<->~B
~B^A<->~A<->C<->~B^~A->~C
A<->~C<->Bv~A->~B^A
A<->~Av~A^B->~C^B^~B
A^C
A<->Cv~A->~B
~A->A^~B->~Av~Cv~C
BvA<->~A^C
~C^~B^~BvC->~C->A
~Cv~C^A^~A->~A
~C^~B^~A^C^~A<->A->~B
B<->~A->~C^B->C^A<->A
~A^A
A^~CvBvA
~B<->A->A^Bv~B
B<->A
A^C^~C
A<->A^~Bv~A
Cv~A->~B
~Cv~A^C<->C^Av~C->A
~Av~Av~A<->~B
B->BvA<->~Cv~B^~C
~CvC^C
B^~A
~B^BvA^C<->~B->A
A^A<->~CvC
~BvB
~Bv~Bv~C^~AvCv~A->A
B<->Cv~B
~C<->A^C^A<->~B
~CvC^~B->~A->~B
~AvB
B<->~A<->B
~A<->~A->C^~Cv~C^C
~C^~BvB^~Av~B<->B
B^B->~C<->Cv~A
B<->C->A<->BvA<->~B^B
~B<->C
~B<->~B^~C->~Cv~C
C<->Bv~C<->~A->C->A<->A
B^~B->~B<->B
BvB->~B->~C->~B^~A^B
~A<->~A<->C
C<->~C^~Cv~B->~Cv~C<->C
B<->B
BvCvB->~B
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~C->B^A->~A->Av~B
Av~C<->~C<->~A
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BvC->B<->C->~B^~C<->~B
Av~C<->Cv~B->C
~A<->B^~B
C<->CvC^~C
C<->C^~CvC^B->B^B
BvB<->~Cv~A^~A
A^~A
~B^A^~A^~A->B
C<->BvC^~B
~A<->~B<->~A^~C<->A<->B
~B^C<->C<->~B
C<->Av~C^~B<->B->~B
C->~C->~C<->AvC
C->~Bv~C->B->BvBv~B
~BvC->~C->~B<->~A
~B<->A^~C<->~A
C^~CvC->B
Cv~C
Cv~B<->B->C^~A->~A
~A<->~BvBvA^~B^C<->A
B->B<->B^~A^~C->B
~B->~B^C^C^~B->Cv~A
Cv~AvB<->B
~A<->~Av~BvC
~C->~C
BvB^~C^~B
~A->B
B^B
B^~A->B<->A->~Av~A
B^A->~A<->C
B^~A<->B<->~B
~AvB<->~C<->B
CvCvC->A^A->C^~A
A<->~CvA^C
C<->~Av~A->~AvAvC->A
~B<->~C->~A->C^B<->~Bv~A
A^CvA->~C<->~CvAv~B
~A^~C<->C
~C->A<->~B
~B^~A<->~C->B
B^~C<->~C^~BvC
CvBv~B<->B<->C
~C^~A<->C<->B->~B
B<->B^A<->~A^~B<->~A->C
~C<->C<->Av~C<->~A
CvB->A
Av~B
~C<->~AvB^B
C^~C->B->C^~A^C
~C^AvB<->A
~Av~A
C^Bv~A^~B
A^C<->A
~CvCvA
C<->~Bv~B^~C->~B<->C
~B->A->A->~BvA
C^C<->~CvA
~C<->B->A->B
~AvA^~B^~B^~A
A<->~A<->C<->~B^~A
C<->C
Av~A^AvC
~B->~B->A
~C->B->~Av~C
~Cv~A^B<->~A
~C^~BvC
~C->~A^~A^C^A<->C->~C
AvC
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A->~Av~A->~Bv~C->A<->C
~AvBv~C^B->~A->C->A
A^Cv~A
B<->BvB
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~B<->~C->C^~A^~B->~Cv~C
~CvA^~B<->~C<->C^~B
~BvC->~A<->B->~Av~C^~A
B^~Bv~A<->B
~CvB<->~C->~B<->~C->A
~A->C^A^B->~C
~B->~A^~B->C^Cv~A<->~C
~C^~A<->C
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CvB->~B<->A->Cv~A
BvA->~Cv~C->B
~B->~B^~C^~A->~B
Bv~B->~A
~C^~B^~C<->A
~B^B->~BvB->~B
Av~B->AvB<->~B^~C
A<->B<->~B<->~A
~B->~B->~Cv~B
B<->C^A^~Av~B
~AvC<->~A->~C
~A<->A<->~A
A->~A^C->~C
~C->~A^Bv~C->C->C^~B
A^B<->AvA
~B->Bv~B^~CvCvC
~A->C<->~B<->A^A->A
C^A<->C^~A
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C->C->B<->~A
A->A<->~A->~A
~B<->~A->~C^B->C->B
~C->B<->~C->C<->C^~C
C->~A<->A^B^B
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~Av~A->~AvCv~B
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BvC
~B<->~C->Av~Cv~A<->AvB
~B<->C^C^~C
BvA
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B^~A^~AvBvBv~AvA
C<->~A<->B
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A^BvA
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C->~A^B
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Cv~B
A->B^~C<->AvC
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C<->A
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B->~C<->~Av~B
A^~AvB^~AvBvC^~C
~C->B^~A^~Cv~A
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~BvA
B<->~B<->~B^A^A<->C->B
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~A^~A
B^~B^B->A<->~B
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C^~B<->C->~CvA^B^~B
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CvB->A<->B
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C->~Av~Cv~B<->Av~B
~A^~B<->~C->~A->C->A
B->C->Cv~A->~C^A
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~Bv~B<->A->~Av~BvA
~B^~B^C->~B->~B<->A
~B->~C->A^A<->A<->C
A->A^C^A
~C<->C^B->~B<->~A^B->~A
B<->A^~A
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