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Byju's Answer
Standard XII
Mathematics
Power Set
If A=ϕ, the...
Question
If
A
=
ϕ
, the empty set, then write the number of elements in
P
(
A
)
.
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Solution
n(A)=0
so P(A) contains
2
0
=1
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0
Similar questions
Q.
When A = ϕ, then the number of elements in P(A) is ____________.
Q.
If
A
=
{
ϕ
,
{
(
ϕ
)
}
}
, then the power set
P
(
A
)
of
A
is
Q.
Let the number of elements in a set
′
A
′
be
′
n
′
.
A set
′
C
′
is defines such that the
C
=
{
(
x
,
y
)
|
x
,
y
∈
P
(
A
)
and
x
∩
y
=
ϕ
}
,
where
P
(
A
)
is power set of
′
A
′
,
then cardinal number of
′
C
′
is
Q.
If A and B are two non-empty sets having n elements in common, then what is the number of common elements in the sets
A
×
B
and
B
×
A
?
Q.
For a non-empty set
X
, if operation
∗
:
P
(
X
)
×
P
(
X
)
⇒
P
(
X
)
is defined as
A
∗
B
=
(
A
−
B
)
∪
(
B
−
A
)
,
∀
A
,
B
∈
P
(
X
)
then show that empty set
ϕ
is the identity for
∗
,
and all elements
A
of
P
(
X
)
are invertible with
A
−
1
=
A
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