Answers for 5-5 Practice Problems

A

B

(A

•

B)

v

~

B

~

B

(A

~

B)

T

T

T

F

F

T

F

T

T

T

F

T

F

F

T

F

F

T

T

T

Valid

X

Y

Z

Z

(~

Z

•

Y)

X

•

(Z

v

X)

~

Y

v

X

~

[~

(~

Z

Y)

v

X]

T

T

T

F

T

T

F

T

T

F

F

T

T

F

T

F

T

F

T

T

F

T

F

F

T

T

T

F

F

T

T

F

F

F

T

F

T

F

F

F

F

T

F

F

T

F

F

T

T

F

F

F

T

F

T

F

Invalid

C

D

E

~

(C

•

D)

E

C

•

(D

v

~

E)

~

[

(C

~

D)

v

C]

D

~

C

(E

v

D)

~

E

T

T

T

T

T

F

F

F

T

T

F

T

T

F

F

T

T

F

T

T

F

F

T

F

T

F

F

F

T

F

T

T

F

T

T

T

F

F

T

F

F

T

F

F

F

F

T

T

F

F

T

T

F

F

F

F

F

F

F

F

F

F

F

T

Valid

G

H

G

H

~

(H

v

G)

~

H

G

~

G

•

H

T

T

T

F

F

F

T

F

F

F

T

F

F

T

T

F

T

T

F

F

T

T

F

F

Valid

A

B

~

{

[(A

~

B)

v

~

B]

~

A}

~

B

[A

•

(~

B

A)]

(~

B

•

B)

v

A

T

T

F

F

T

T

F

T

T

T

F

T

F

T

F

F

F

F

F

F

Valid

X

Y

Z

[(Z

Y)

~

Z]

v

X

~

(~

Y

•

X)

(X

v

Y)

v

~

Z

~

Z

~

Y

T

T

T

T

T

T

T

T

T

F

T

T

T

F

T

F

T

T

F

T

T

T

F

F

T

F

T

T

F

T

T

F

T

T

T

F

T

F

T

T

T

F

F

F

T

T

T

F

T

F

F

F

T

T

T

T

Invalid