1
CS/MA320 HW2 Solutions
Quiz 2 will be on this material on Wednesday, Oct. 30, in the first 20 minutes.
First, I list Reading Assignment & Solved Exercises to look at.
2.1 Reading: Study everything but skip Exercise 20.
Exercises With So
luti
ons in 2.1:
pg. 119:
5.a-d, 7.a-e,
15.
Exercises For You To Solve in 2.1
: pg. 119: 2.a, 8.a-c&g, 16, 20.
Solutions for 2.1
.
2
. There are multiple correct answers; I give one or two.
2.a
. {3n | n = 0, 1, 2, 3, 4} or {x | x
¸
N
À
x is a multiple of 3
À
0
≤
x
≤
12}. I ADD A FEW OTHER SOLUTIONS.
2.b
. {x | -3
≤
x
≤
3
À
x
¸
Z
}, or one can use English: {x | -3
≤
x
≤
3} where the domain of x is the set of
integers.
2.c
. Possible answer: {x | x is a letter of the word
monopoly
other than
l
or
y
}.
8.a
. True.
8.b
. True.
8.c
. False: see 8.a.
8.g
. False. The two sets are equal.
16
. Since the empty set is a subset of every set, we just need to take a set B that contains
∅
as an
element. Thus we can let A =
∅
and B = {
∅
} as the simplest example. We could also let A = {1,
2) and B = {1, 2, {1, 2)), for example.
20
. The union of all sets in the power set of S is S. Thus we can recover the set S from P(S) and
the set T from P(T) and if P(S) = P(T) then S = T.
2.2 Reading: Skip last part on Computer Representation.
Exercises With So
luti
ons in 2.2:
pg. 130: 3, 7, 15.a-b, 35
Exercises For You To Solve in 2.2
: pg. 130: 4, 14 (Hint: consider (A - B)
∪
(A
∩
B) and another
union of two sets considered), 36.
Solutions for 2.2
.
4
. Note that A
⊆
B (in fact A is a
proper
subset of B: A
⊂
B).
4.a
. A
∪
B = B = {a, b, c, d, e, f,
g, h}.
4.b
. A
∩
B = A = {a, b, c, d, e}.
4.c
. No elements in A fail to be in B, so A - B =
∅
.
4.d