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Mathematics
Problem
Suppose
U
=
{
x
∈
Z
∣
0
≤
x
≤
40
}
U = \{x \in \mathbb{Z} \mid 0 \le x \le 40\}
U
=
{
x
∈
Z
∣
0
≤
x
≤
40
}
,
P
=
{
factors of
28
}
P = \{\text{factors of } 28\}
P
=
{
factors of
28
}
, and
Q
=
{
factors of
40
}
Q = \{\text{factors of } 40\}
Q
=
{
factors of
40
}
. a. a List P and Q. b. b Find
P
∩
Q
P \cap Q
P
∩
Q
. c. c Find
P
∪
Q
P \cup Q
P
∪
Q
. d. 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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