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Mathematics
Mathematics
Problem
Suppose
U
=
{
x
∣
x
is a positive integer less than
100
}
U = \{x \mid x \text{ is a positive integer less than } 100\}
U
=
{
x
∣
x
is a positive integer less than
100
}
. Let
A
=
{
multiples of
7
in
U
}
A = \{\text{multiples of } 7 \text{ in } U\}
A
=
{
multiples of
7
in
U
}
and
B
=
{
multiples of
5
in
U
}
B = \{\text{multiples of } 5 \text{ in } U\}
B
=
{
multiples of
5
in
U
}
. a. How many elements are there in: - A - B -
A
∩
B
A \cap B
A
∩
B
-
A
∪
B
A \cup B
A
∪
B
? b. Show that
n
(
A
∪
B
)
=
n
(
A
)
+
n
(
B
)
−
n
(
A
∩
B
)
n(A \cup B) = n(A) + n(B) - n(A \cap B)
n
(
A
∪
B
)
=
n
(
A
)
+
n
(
B
)
−
n
(
A
∩
B
)
.
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