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Mathematics
Mathematics
Problem
Suppose
U
=
Z
+
U = \mathbb{Z}^+
U
=
Z
+
,
P
=
{
x
∈
Z
+
∣
9
≤
x
<
16
}
P = \{x \in \mathbb{Z}^+ \mid 9 \le x < 16\}
P
=
{
x
∈
Z
+
∣
9
≤
x
<
16
}
, and
Q
=
{
2
,
4
,
5
,
11
,
12
,
15
}
Q = \{2, 4, 5, 11, 12, 15\}
Q
=
{
2
,
4
,
5
,
11
,
12
,
15
}
. (a) List
P
P
P
. (b) Find
P
∩
Q
P \cap Q
P
∩
Q
. (c) Find
P
∪
Q
P \cup Q
P
∪
Q
. (d) Show that
n
(
P
∪
Q
)
=
n
(
P
)
+
n
(
Q
)
−
n
(
P
∩
Q
)
n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)
n
(
P
∪
Q
)
=
n
(
P
)
+
n
(
Q
)
−
n
(
P
∩
Q
)
.
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