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Byju's Answer
Standard XII
Mathematics
Cardinality of Sets
If A is the s...
Question
If
A
is the set of odd prime numbers and
B
=
{
x
∈
Z
:
−
6
<
2
x
−
5
3
≤
7
and
−
4
≤
x
−
7
2
<
4
}
,
then the value of
n
(
A
∩
B
)
is
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Solution
A
=
{
3
,
5
,
7
,
11
,
13
,
17
,
19
,
.
.
.
}
B
=
{
x
∈
Z
:
−
6
<
2
x
−
5
3
≤
7
and
−
4
≤
x
−
7
2
<
4
}
⇒
−
6
<
2
x
−
5
3
≤
7
⇒
−
18
<
2
x
−
5
≤
21
⇒
−
13
<
2
x
≤
26
⇒
−
13
2
<
x
≤
13
.
.
.
(
1
)
and
−
4
≤
x
−
7
2
<
4
⇒
−
8
≤
x
−
7
<
8
⇒
−
1
≤
x
<
15
.
.
.
(
2
)
From
(
1
)
and
(
2
)
,
−
1
≤
x
≤
13
B
=
{
−
1
,
0
,
1
,
.
.
.
,
12
,
13
}
A
∩
B
=
{
3
,
5
,
7
,
11
,
13
}
∴
n
(
A
∩
B
)
=
5
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0
Similar questions
Q.
Let
A
=
{
x
:
2
<
|
x
|
≤
5
and
x
∈
Z
}
and
B
be the set of values of
a
for which the equation
∣
∣
|
x
−
1
|
+
a
∣
∣
=
4
can have real solutions. Then
n
(
A
∩
B
)
is
Q.
If
A
=
{
x
:
x
2
−
4
≤
0
,
x
∈
Z
}
and
B
=
{
y
:
y
2
−
9
≥
0
,
y
∈
Z
}
, then
n
(
A
∩
B
)
is equal to
Q.
Let
A
=
{
x
:
2
<
|
x
|
≤
5
and
x
∈
Z
}
and
B
be the set of values of
a
for which the equation
∣
∣
|
x
−
1
|
+
a
∣
∣
=
4
can have real solutions. Then
n
(
A
∩
B
)
is
Q.
Let
Z
be the set of all integers.
A
=
{
(
x
,
y
)
∈
Z
×
Z
:
(
x
−
2
)
2
+
y
2
≤
4
}
,
B
=
{
(
x
,
y
)
∈
Z
×
Z
:
x
2
+
y
2
≤
4
}
and
C
=
{
(
x
,
y
)
∈
Z
×
Z
:
(
x
−
2
)
2
+
(
y
2
−
2
)
2
≤
4
}
If the total number of relations from
A
∩
B
to
A
∩
C
is
2
p
, then the value of
p
is
Q.
If
A
=
{
x
∈
N
:
log
2
x
+
3
log
2
x
<
4
,
x
>
1
}
and
B
=
{
x
∈
Z
:
(
4
−
x
2
)
(
x
2
−
8
x
+
15
)
≥
0
}
,
then the number of subsets of the set
(
A
∪
B
)
−
(
A
∩
B
)
is
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