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Announcements
Midterm 1 is on Wednesday
Time:
7pm to 9pm
Location:
141 Wohlers Hall
Lecture on Wednesday is optional: examrelated Q&A
Extra office hour on Wednesday: 11am to 12pm
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View Full Document Another False Proof
“
Claim
”:
P
(
A
)
∪
P
(
B
)
=
P
(
A
∪
B
)
“
Proof
”: Let S
∈
P(A)
∪
P(B). Then S
∈
P(A) or S
∈
P(B)
So
S
⊆
A
or
S
⊆
B
So
S
⊆
A
∪
B
Hence
S
∈
P
(
A
∪
B
)
Let
S
∈
P
(
A
∪
B
)
So
S
⊆
A
∪
B
So
∀
x
,
x
∈
S
→
x
∈
A
∪
B
∀
x
,
x
∈
S
→
x
∈
A
or
x
∈
B
S
⊆
A
or
S
⊆
B
So
S
∈
P
(
A
)
or
S
∈
P
(
B
)
So
S
∈
P
(
A
)
∪
P
(
B
)
Functions
In a programming language like C or Java, we declare functions like this:
int f(int x) {
// int argument, int return value
return 2*x;
}
In general, a function each argument a unique return value
The set from which arguments are drawn is called the
domain
The set from which return values are drawn is called the
codomain
In our example, arguments and return values are both
int
s
So,
f
:
Z
→
Z
and is defined by
f
(
x
) = 2
x
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View Full Document Functions contd.
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This note was uploaded on 12/24/2010 for the course CS CS 173 taught by Professor Fleck during the Spring '10 term at University of Illinois, Urbana Champaign.
 Spring '10
 fleck

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