北航数理逻辑考试题

100

(1%×20=20%)

.

b

1.∩∩(2,0)=2.a

m

n

a

b

3.

a={{ω+3},{{ω}}},∪a=.

,∪3a=

4.5.6.7.

ω3=

.

µ

a,b,

f

a

b

f

a

b

8.

{}(

).3

ω

ω+2

9.

2

(2%×5=10%)

1.

2.p∧q

4

1

3.”

”

4.5.

(4%×6=24%)

1.s

t∧( sP(t,s))

t,

2.3.

A∨B

4.5.b2(x)=26.

i-

i-

(15%)

1.

(1)(2%);

(2)(2%).

2.”

”

(3%)

3.

(4%)

( y)P(x,y)

( x)( y)P(x,y)( x)( y)P(x,y)→( y)P(y,y)

(k5)

( y)P(y,y)

MP

( y)P(x,y) K( y)P(y,y),

K( y)P(x,y)→( y)P(y,y)

2

v

( xiA).

”

A

B

”

4.

xi

A(xi)

xj

A(xi)

(( xi)A(xi)→

( xj)A(xj))(4%).

(4%×6=24%)

ω+1

1.ω

(

).

2.b,b

3.4.ω=∪ω.

5.

A,B,C,

6.

x

On

P(x)

3

P(b)

A∈B∧B∈C∧C∈A

(7%)

1.

(k1)(A→(B→A))

(k2)(A→(B→C))→((A→B)→(A→C))(k3)(～A→～B)→(B→A)2.

(k4)(( xi)A→A),xi

A

(k5)(( xi)A(xi)→A(t)),

A(xi)

L

t

L

xi

(k6)( xi)(A→B)→(A→( xi)B),Axi

3.

(E7)(x1=x1)

(E8)(tk=u→(fin(t1,...,tk,...,tn)=fin(t1,...,u,...,tn))),

fin

L(E9)(tk=u→(Ani(t1,...,tk,...,tn)→Ani(t1,...,u,...,tn))),

Ani

L

4.

(N1)( x

1)～(x1=0)

(N2)( x

1)( x2)(x1=x2→x1=x2)(N3)( x1)(x1+0=x1)

(N4)( x

1)( x2)(x1+x2=(x1+x2))(N5)( x1)(x1×0=0)

(N6)( x1)( x2)(x1×x

2=(x1×x2)+x1)

(N7)A(0)→(( x1)(A(x1)→A(x

1))→( x1)A(x1)),x1

A(x1)

4

A(xi)

t1,...,tn,ut1,...,tn,u

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