Sistemas Dicotômicos

Sistemas Dicotômicos

1) Dar as seguintes expressões algébricas dos circuitos desenhados:

g)

Resposta: ( a . b + a ’ . b ) + (a ‘ . b’ )

h)

Resposta: [ ( a . b + c . a ) . d + b ] + [ ( b + c ) . ( d . c + b . d ) ]

l)

Resposta: ( a . b’ . c + a’ . b . c ) + ( a . b’ . c + a’ . b . c’ ) + ( a . b .c’ + a’ . b . c )

1) Desenhar os circuitos cujas ligações são dadas pelas expressões

g) ( p + q ) . ( p + q’ + r’)

h) ( a + b . c ) . ( a’ . b’ + c’ ) + a’ . b’ . c’

1) Desenhar os diagramas de Euler – Venn para mostrar:

e) ( p’ + q’ ) . r

p’ q’ r

( p’ + q’ ) ( p’ + q’ ) . r

f) ( p’ + q’ ) . r

p q r

( p + q ) ( p’ + q’ ) . r

Operações Lógicas sobre Proposições

9) Se V(p) = V(q) = 1 e V(r) = V(s) = 0, determinar os valores lógicos das seguintes proposições:

a) p’ + r

p r p’ p’ + r

1 0 0 0

b) [ r + ( p → s ) ]

r p s p → s [ r + ( p → s ) ]

0 1 0 0 0

c) [ p’ + ( r . s ) ‘ ]

p r s p’ r . s ( r . s ) ‘ [ p’ + ( r . s ) ‘ ]

1 0 0 0 0 1 0

d) [ q ↔ ( p’ . s ) ] ‘

p q s p’ ( p’ . s ) q ↔ ( p’ . s ) [ q ↔ ( p’ . s ) ] ‘

1 1 0 0 0 0 1

e) ( p ↔ q ) + ( q → p’ )

p q p’ ( p ↔ q ) ( q → p’ ) ( p ↔ q ) + ( q → p’ )

1 1 0 1 0 1

f) ( p ↔ q ) . (r’ → s )

p q r s r’ ( p ↔ q ) (r’ → s ) ( p ↔ q ) . (r’ → s )

1 1 0 0 1 1 0 0

g) { [ q’ . ( p . s’ ) ] }

p q s q’ s’ ( p . s’ ) { [ q’ . ( p . s’ ) ] }

1 1 0 0 0 0 0

h) { p’ + [ q . ( r → s’ ) ] }

p q r s p’ s’ ( r → s’ ) [ q . ( r → s’ ) ] { p’ + [ q . ( r → s’ ) ] }

1 1 0 0 0 1 1 1 1

Construção da Tabela –Verdade

1) Construir as tabelas-verdade das proposições seguintes:

a) ( p . q )’

p q q‘ p . q ( p . q )’

0 0 1 0 1

0 1 0 0 1

1 0 1 1 0

1 1 0 0 1

b) ( p → q’)’

p q q‘ p → q’ ( p → q’ )’

0 0 1 1 0

0 1 0 1 0

1 0 1 1 0

1 1 0 0 1

d) p’ → ( q → p )

p q p’ ( q → p ) p’ → ( q → p )

0 0 1 1 1

0 1 1 1 1

1 0 0 0 0

1 1 0 1 1

e) ( p → q) → q . p

p q ( p → q) q . p ( p → q) → q . p

0 0 1 0 0

0 1 1 0 0

1 0 0 0 1

1 1 1 1 1

f) q ↔ q’ . p →

p q q’ q’ . p q ↔ q’ . p

0 0 1 0 1

0 1 0 0 0

1 0 1 1 0

1 1 0 0 0

g) ( p ↔ q’ ) → q + p

p q q’ ( p ↔ q’ ) q + p ( p ↔ q’ ) → q + p

0 0 1 0 0 1

0 1 0 1 1 1

1 0 1 1 1 1

1 1 0 0 1 1

h) ( p ↔ q’) → p’ . q

p q p’ q’ ( p ↔ q’) p’ . q ( p ↔ q’) → p’ . q

0 0 1 1 0 0 0

0 1 1 0 1 1 1

1 0 0 1 1 0 0

1 1 0 0 0 1 1

m) ( p+ q → r ) + ( p’ ↔ q + r’)

p q r p’ r’ p+ q ( p+ q → r ) q + r’ ( p’ ↔ q + r’) ( p+ q → r ) + ( p’ ↔ q + r’)

0 0 0 1 1 0 1 0 1 1

0 0 1 1 0 0 0 0 0 0

0 1 0 1 1 1 1 1 1 1

0 1 1 1 0 1 1 1 1 1

1 0 0 0 1 1 1 1 1 1