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Problem
Problem
Let
U
=
{
x
∈
Z
+
∣
x
≤
30
}
U = \{x \in \mathbb{Z}^+ \mid x \le 30\}
U
=
{
x
∈
Z
+
∣
x
≤
30
}
,
P
=
{
factors of 24
}
P = \{\text{factors of 24}\}
P
=
{
factors of 24
}
, and
Q
=
{
factors of 30
}
Q = \{\text{factors of 30}\}
Q
=
{
factors of 30
}
. List the elements of: a.
P
P
P
b.
Q
Q
Q
c.
P
∩
Q
P \cap Q
P
∩
Q
d.
P
∪
Q
P \cup Q
P
∪
Q
e. 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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