3
5. TRUE or FALSE. (If true, PROVE it. If false, give a COUNTER EXAMPLE.)
If A is a finite set and b is an element of A, then
'-"
T
--;:. {o- E SA I o-(b)
= b}
IS a group.
Trut?c:..:--(d,IIvl'
,
r,,~(~J
.:-:--
-r~
V, 'l' €-
it
I
trot (k)
(Ie T i ~
a-(Io) ~
h
-=-
r;r{1.) -=
J, ,', (/<>Zf- T
s"o (f"-tfhJ:::: ~-((6)
So
J, ~(T-I(t,)
I~(.{J v-f t- T
T f <)
6.
'
'"
hoT
e~/tJ
be {dttSIt
~fT
TRUE or FALSE. (If true, PROVE it. If false, give a COUNTER EXAMPLE.)
If A is a finite set, B is a subset of A, and b is an element of B, then
T~
{o-E SA
I o-(b)
E B}
IS a group.
Eq(~
f~
b<,f
Thttj
..............
Tok
fl'r
,4::-11r451
tf 0"rfJ. 23)
Q -jJ) ~ T
"?4 -("1
(T L?
B==-<ilft?
T ~ hDi C(oJ4!J.
i j';
be{;tqjz
b~1
,>;'IE~
<r( I)
rj'-(/);::3 f/ B
"'.2..
<'-/5