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32
Solutions to Exercises
Exercises
2.2
1.
(a)
[BB]
A
=
{I, 2, 3,4,5, 6}.
B
=
{I, 0,1,2,3,4, 5},
C
=
{O, 2, 2}.
(b)
AU C
=
{2,0, 1, 2,3,4,5,6}.
B
n
C
=
{0,2},
B" C
=
{I, 1,3,4, 5}.
A
EI1
B
=
{1,6,0},
C
x
(B
n
C)
=
{(O, 0), (0,2), (2,0), (2,2), (2,0), (2, 2)},
(A" B)
"
C
=
{6},
A
"
(B
"
C)
=
{2, 6},
(B
U 0)
n
{0}
=
0.
(c)
S
=
{(I, 1), (2,0), (3, 1), (4,2), (5, 3), (6, 4)};
T
=
{(I, 2), (2, 2)}.
2.
(a) [BB]
S
n
T
=
{v'2, 25}.
S
U
T
=
{2, 5, v'2,
25,11",
~,4,
6,
n,
T
x
(S
n
T)
=
{(4, v'2), (4,25), (25, v'2), (25,25), (v'2, v'2),
(v'2,25),(6,v'2),(6,25),(~,v'2),(~,25)}.
(b)
[BB]
Z U
S
=
{v'2,
11",~,
0,1,
1, 2, 2,
... };
Z
n
S
=
{2, 5, 25};
Z
UT
=
{v'2,
~,O,
1, 1,2,
2,
... }; Z
nT
=
{4,25,6}.
(c) Z n
(S
U
T)
=
{2, 5, 25, 4, 6}
=
(Z n
S)
U (Z n
T).
The two sets are equal.
(d) Z U
(S nT)
=
{v'2,0, 1, 1,2,
2,
... }
=
Zu {v'2}
=
(ZU
S)
n (Z U
T).
The two sets are equal.
,
3. (a) [BB] {I, 9, 0, 6, 7};
(b) {4, 6, 5};
(c) {O, I}.
4. A
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 Summer '10
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 Graph Theory

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