Homework #2 answers
1.7
Original
Rotated 90
degrees
Rotated 180
degrees
Rotated 270
degrees
1
F
F
F
F
2
F
F
F
F
3
T
F
F
T
4
F
F
T
T
5
T
F
F
F
6
F
F
T
F
For Sentence 7, something like
SameCol(a,d)
will do, anything that yields the same truth value when
viewed from the front and the back.
For sentence 8, we need a relation which is true when viewed from just one direction. One such relation
is
Backof
and we need a relation which is true when viewed 90 degrees turned, so
Backof(d,e)
will do.
For sentence 9, we need a case in which precisely three Ts occur. No matter what you do, you can
wither get one T, two Ts or four Ts, but no three Ts, so line 9 must be kept blank.
1.8
a)
GaveScruffy(max, max)
GaveScruffy(claire, claire)
GaveScruffy(max, claire)
GaveScruffy(claire, max)
b)
Gave(max, max, max)
Gave(claire, claire, claire)
Gave(scruffy, scruffy, scruffy)
Gave(max, max, claire)
Gave(claire, claire, max)
Gave(scruffy, scruffy, max)
Gave(max, max, scruffy)
Gave(claire, claire, scruffy)
Gave(scruffy, scruffy, claire)