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Byju's Answer
Standard XII
Mathematics
Intersection of Sets
If U= 1,2,3...
Question
If
U
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
}
A
=
{
1
,
2
,
3
,
4
}
and
B
=
{
2
,
4
,
6
,
8
}
. Verify that
(
A
∪
B
)
1
=
A
1
∩
B
1
.
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Solution
given
U
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
}
,A=
{
1
,
2
,
3
,
4
}
,B=
{
2
,
4
,
6
,
8
}
therefore A
∪
B=
{
1
,
2
,
3
,
4
,
6
,
8
}
(
A
∪
B
)
1
=
{
5
,
7
}
A
1
=
{
5
,
6
,
7
,
8
}
,
B
1
=
{
1
,
3
,
5
,
7
,
9
}
therefore
A
∩
B
=
{
5
,
7
}
therefore proved
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Similar questions
Q.
If the lines represented by
a
x
2
+
2
h
x
y
+
b
y
2
=
0
are
u
=
a
1
x
+
b
1
y
=
0
and
v
=
a
2
x
+
b
2
y
=
0
and are coinciding then:
(a)
a
1
b
1
=
a
2
b
2
(b)
a
1
b
1
≠
a
2
b
2
(c)
a
1
a
1
=
b
1
b
1
(d)
a
1
a
1
+
b
1
b
1
=
0
Q.
Prove that the points
(
a
,
b
)
,
(
a
1
,
b
1
and
(
a
−
a
1
,
b
−
b
1
)
are collinear if
a
b
1
=
a
1
b
.
Q.
If the points
(
a
1
,
b
1
)
,
(
a
2
,
b
2
)
and
(
a
1
+
a
2
,
b
1
+
b
2
)
are collinear, then show that
a
1
b
2
=
a
2
b
1
.
Q.
If
U
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
}
,
A
=
{
2
,
4
,
6
,
8
}
and
B
=
{
2
,
3
,
5
,
7
}
verify that
(
A
∪
B
)
′
=
A
′
∩
B
′
Q.
Assertion :Two lines
a
¯
z
+
¯
a
z
+
b
=
0
,
a
1
¯
z
+
¯
a
1
z
+
b
1
=
0
(where
a
,
a
1
∈
C
,
a
,
a
1
≠
0
and
b
,
b
1
∈
R
) are parallel if and only if
a
a
1
is real. Reason: Two lines
a
¯
z
+
¯
a
z
+
b
=
0
,
a
1
¯
z
+
¯
a
1
z
+
b
1
=
0
(where
a
,
a
1
∈
C
,
a
,
a
1
≠
0
and
b
,
b
1
∈
R
) are perpendicular if and only if
a
a
1
is purely imaginary.
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