HW9
P243: 8, 9, 12, 15, 16; P253: 8, 9, 11
P254: 13; P265: 2, 4, 5, 9
P266: 8, 12, 16, 17
ALEX FLURY
batch 1
5.2.8. Suppose f : A B and g : B C .
(a). Prove that if g f is onto, then g is onto.
Proof. Suppose g f is onto. Suppose c C . Since g f is onto,
P13: 2, 3, 4, 6, 7
P24: 2, 4, 5, 6, 8
batch 1
1.1.2. Analyze the logical forms of the following statements.
(a). Either John and Bill are both telling the truth, or neither of them is.
P = John is telling the truth.
Q = Bill is telling the truth.
(P Q) (P
Homework Set 8 Solutions Dai
Kyle Chapman
March 11, 2013
223.4
a
Not an equivalence relation because (1, 0) R but (0, 1) R.
/
b
This is an equivalence relation. The equivalence classes are of the form x + Q for each real number x.
c
This is an equivalence
HW5
P122: 2, 4, 8
4, 5
P122: 18, 20, 21, 23
ALEX FLURY
batch 1
3.3.2. Prove that if A and B \ C are disjoint, then A B C .
Proof. Suppose A and B \ C are disjoint, and let x be an arbitrary element of A B .
Since x A, therefore x B \ C . This means either
Homework Set 4 Solutions
Kyle Chapman
February 6, 2013
93.1
a
The hypothesis is that n is an integer larger than one and that n is not prime. The conclusion is that 2n 1
is not prime. The hypotesis is satised for n = 6 since 6 is greater than one and not
Homework Set 7 Solutions
Kyle Chapman
March 5, 2013
178.2
a
The domain of this function is the set of people who are brothers. The range is the set of people who have
brothers.
b
To nd the domain, we allow y to be any real value, and so y 2 can be any non
P25: 10, 12, 13, 18; P33: 3, 4; P42: 2
P42: 4, 5, 8, 9; P53: 2, 4, 6
P54: 5, 10; P63: 2, 3, 5, 7
batch 1
1.2.10. Use truth tables to check these laws.
(a). The second DeMorgans law.
P
F
F
T
T
T
T
T
F
Q
F
T
F
T
(P
F
F
T
T
Q)
FF
FT
FF
TT
T
T
F
F
P
F
F
T
T
Homework Set 3 Solutions
Kyle Chapman
January 27, 2013
72.2
a
It is not true that there is someone in the freshmen class who doesnt have a roomate.
Everyone in the freshmen class has a roomate.
b
It is not true that both everyone likes someone and noone l
HW6
P143: 2, 7, 8, 10, 14; 6, 7
P133: 6, 7, 10, 22; P161: 9; 6
P170: 4, 5, 6, 9
ALEX FLURY
batch 1
3.5.2. Suppose A, B , and C are sets. Prove that A (B C ) (A B ) C .
Proof. Let A, B , and C be sets, and let x be an arbitrary element of A (B C ). Then
ei
Page 296: 3a:proof: Contradiction. Suppose 6 is a rational number. This means
that there exist q Z + and q Z + such that p = 6. So the set S = cfw_q Z + |( p =
q
q
6) is nonempty. By the well ordering principle we can let q be the smallest element
2
of S