MA2312
Spring 2010
Homework 2
John Iacono
January 28, 2010
Read sections 1.11.7.
1. For each of these expressions, tell me in the simplest way possible what
they evaluate to. For example, if the question is 2+2, you should respond
4, and not 1 + 3, 2 + 2, or
√
4. If the expression makes no sense, answer
“Doesn’t make sense.” Some of this is a review of some math you should
know.
(i)
{
1
,
2
,
3
}
=
{
3
,
2
,
1
}
(ii)
{
1
,
2
,
4
}
(iii)
∅ ∈ {
1
,
2
,
4
}
(iv) 1
∈ {
1
,
2
,
4
}
(v)
∅ ∈ {
1
,
2
,
4
}
(vi)
{
1
} ∈ {
1
,
2
,
4
}
(vii) 1
⊆ {
1
,
2
,
4
}
(viii)
{
1
} ⊆ {
1
,
2
,
4
}
(ix)
{
a, b, c
} ∪ {
b, d
}
(x)
{
a, b, c
} ∩ {
b, d
}
(xi)
{
a, b, c
}  {
b, d
}
(xii)
{
a, b
} × {
1
,
2
}
(xiii) 2
×
8
(xiv)
{
a, b
} × ∅
(xv)
{
a, b
} × {∅}
(xvi) 2
{
1
}
(Your book writes this as
P
(
{
1
}
))
(xvii) 2
{
1
}
×
2
{
2
}
(xviii) 2
1
1
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(xix) 2
1
×
2
2
(xx) log
256
1
65536
(xxi)
d
22
7
e
(xxii)
b
22
7
c
(xxiii)
d
2
e
(xxiv)
b
2
c
(xxv) 34 mod 5
(xxvi) 34

5
(xxvii) 5!
(xxviii)
∑
5
i
=0
i
(xxix)
∑
5
i
=0
1
(xxx)
∑
5
i
=0
x
(xxxi)
Q
500
i
=0
i
(xxxii)
S
3
i
=1
{
2
i
}
(xxxiii)
W
3
i
=1
{
2
i
= 4
}
(xxxiv)
z
∈ {
x

f
(
x
)
}
, where
f
(
x
) is a predicate
(xxxv)
∀
x
[log
c
x
=
log
2
x
log
2
c
]
(xxxvi)
∀
x
[
x
is odd
→
x
is seven]
(xxxvii)
∀
x
[
x
is seven
→
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 Spring '10
 JohnIacono
 Math, Integers, internet connection, John Iacono

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