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Mathematics
Mathematics
Problem
Suppose
U
=
Z
+
U = \mathbb{Z}^+
U
=
Z
+
,
P
=
{
multiples of 4 less than 50
}
P = \{\text{multiples of 4 less than 50}\}
P
=
{
multiples of 4 less than 50
}
, and
Q
=
{
multiples of 6 less than 50
}
Q = \{\text{multiples of 6 less than 50}\}
Q
=
{
multiples of 6 less than 50
}
. a. List
P
P
P
and
Q
Q
Q
. 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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