As usual, you
will
also be tested on previous material as well – I'd make sure that you
can
do problems like those on the previous quiz. There's also plenty of
problems
in the book – pretty much all of the problems in the sections of Ch 4
and
6 that we read have arguments to work on (some valid and some invalid).
1. Translate
the following between colloquial English and the language of TW
as
appropriate:
(i) b is neither a medium
cube
nor a large tetrahedron.
(ii) There is a
dodecahedron
adjoining c.
(iii) Only if there
is a
dodecahedron adjoining c is c a cube.
(iv) c is between b and a large cube.
(v)
If
b is not in
back
of c then
nothing
is.
(vi)
All the small dodecahedra are behind c.
(vii) Ez(Small(z) ^ Dodec(z)
^
Behind(z, c))
(viii) Not all the
small
dodecahedra are behind c.
(ix) No
small dodecahedra are behind c.
(x) All the cubes
being
large is a necessary condition for everything being large.
2. Evaluate the
truth-values
of the following in World A:
(i) ExCube(x) –> AxCube(x)
(ii)
Ex(Cube(x) ^ RightOf(a,x))
(iii) Ex(Cube(x) ^
RightOf(x,a))
(iv) Ax((Dodec(x) ^
Small(x))
–> Adjoins(x,b))
(v) Ex(Cube(x) ^ Dodec(x))
3. Give formal proofs of the following (you could also do truth tables
and
informal proofs for practice):
(i) P ^ Q, (P –> R) v (Q –> R) therefore R
(ii) P
–>
(Q –> R) therefore (P
^ Q) –> R
(iii) P
–>
Q, Q –> R, ¬R therefore ¬P
(iv) P
–>
Q therefore P –>
(Q
v R)
(v) P ^
(Q v
R) therefore (P ^
Q) v
(P ^ R)