Truth in a model

Given the model below, determine whether each sentence comes out true or false.

UD	=	{Jet, Faye, Spike}
extension(A)	=	{Jet, Spike}
extension(B)	=
extension(F)	=	{Spike, Faye}
extension(S)	=	UD
extension(R)	=	{, }
referent(j)	=	Jet
referent(s)	=	Spike

1) (Bj Fj)

True in the model

False in the model

2) Rjs

True in the model

False in the model

3) (Ss & Bs)

True in the model

False in the model

4) xAx

True in the model

False in the model

5) xSx

True in the model

False in the model

6) xRsx

True in the model

False in the model

7) (xFx & xFx)

True in the model

False in the model

8) x(Fx & Fx)

True in the model

False in the model

9) x(Bx Fx)

True in the model

False in the model

10) xyRxy

True in the model

False in the model

Contingent sentences

Show that the sentence is contingent by constructing two models. Make it true in the first model and false in the second.

11a)

(xPx & Jd)

Domain:

P(_):

J(_):

d:

11b)

(xPx & Jd)

Domain:

P(_):

J(_):

d:

Show that the sentence is contingent by constructing two models. Make it true in the first model and false in the second.

12a)

(xPx xPx)

Domain:

P(_):

12b)

(xPx xPx)

Domain:

P(_):

Invalid arguments

Show that the argument is invalid by constructing a model in which the premises are true and the conclusion is false.

13)

Fa, Ka Ta

Domain:

F(_):

K(_):

T(_):

a:

Show that the argument is invalid by constructing a model in which the premises are true and the conclusion is false.

14)

x(Px Qx) xQx

Domain:

P(_):

Q(_):

Show that the argument is invalid by constructing a model in which the premises are true and the conclusion is false.

15)

(Ma xMx), (Ma Na) xMx

Domain:

M(_):

N(_):

a:

Show that the argument is invalid by constructing a model in which the premises are true and the conclusion is false.

16)

xPx, xQx x(Px & Qx)

Domain:

P(_):

Q(_):