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Question
Mathematics
Universal set, U = x | x5 - 6x4 + 11x3 - 6x2 = 0 A = x | x2 - 5x + 6 = 0 B = x | x2 - 3x + 2 = 0 What is (A ∩ B)' equal to ?
Q. Universal set,
U
=
{
x
∣
x
5
−
6
x
4
+
11
x
3
−
6
x
2
=
0
}
A
=
{
x
∣
x
2
−
5
x
+
6
=
0
}
B
=
{
x
∣
x
2
−
3
x
+
2
=
0
}
What is
(
A
∩
B
)
′
equal to ?
3720
205
Sets
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A
{1, 3}
13%
B
{1, 2, 3}
25%
C
{0, 1, 3}
44%
D
{0, 1, 2, 3}
19%
Solution:
U
=
{
x
:
x
5
−
6
x
4
+
11
x
3
−
6
x
2
=
0
}
Solving for values of x, we get
U
=
{
0
,
1
,
2
,
3
}
A
=
{
x
:
x
2
−
5
x
+
6
=
0
}
Solving for values of x, we get
A
=
{
2
,
3
}
and
B
=
{
x
:
x
2
−
3
x
+
2
=
0
}
Solving for values of x, we get
B
=
{
2
,
1
}
A
∩
B
=
{
2
}
∴
(
A
∩
B
)
′
=
U
−
(
A
∩
B
)
=
{
0
,
1
,
2
,
3
}
−
{
2
}
=
{
0
,
1
,
3
}