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Section 2.2
(c) Negation:
M
~
P;
No converse since the statement is not an implication.
(d) Negation:
(M
U
CS)
nP
rzr
c
;
Converse:
TC·~
(M
U
CS)
n
P.
(e) Negation:
(M
U
CS)
n
P
n
T
=1=
0; Converse
T
C
~
(M
U
CS)
n
P.
12.
(a)
[BB] En
P
=1=
0
(b)
OEZ, N (c) N
~
Z
(d) . Z
rz
N
(e)
(P , {2})
~
F
(f)
2 E
En
P
(g)
En P
=
{2}
13. (a)
[BB]
Since
A_3
~
A3, A3
U
A_3
=
A3~
(b) Since
A_3
~
A3, A3
n
A_
3
=
A_
3
..
(c)
A3
n
(A_3)C
=
{a
E Z
13
<
a::;
3}=
{2,1,0, 1,2,3}.
(d) Since
Ao
~
Al
~
A2
~
A3
~
A4,
we have
ni=o
Ai
=
Ao.
33
14.
[BB]
Region 2 represents
(AnC)
,S.
Region 3 represents
AnBnC;
region 4 represents
(AnB)
,C.
15.
(a)
B
A
.
(b)
i.
(A
U
B)
n
C
=
{5, 6}
ii.
A,
(B' A)
=
A
=
{1,2,4, 7,8,9}
iii.
(AUB),
(AnC)
= {1,2,3,4,9}
iv.
A
EB
C
= {I, 2,4,7,8,
9}
v.
(A
n
C)
x
(A
n
B)
= {(5, 1), (5,2), (5,4), (6, 1), (6,2), (6, 4)}
16.· (a)
[BB]
A
~
B,
by Problem 7;
(b)B·~
A,
by PAUSE 4 with
A
and
B
reversed.
17.
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 Summer '10
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 Graph Theory

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