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Mathematics
Problem
3. Given a non empty set X , consider
P
(
X
)
\mathrm{P}(\mathrm{X})
P
(
X
)
which is the set of all subsets of X . Define the relation
R
R
R
in
P
(
X
)
P(X)
P
(
X
)
as follows: For subsets
A
,
B
\mathrm{A}, \mathrm{B}
A
,
B
in
P
(
X
)
,
A
R
B
\mathrm{P}(\mathrm{X}), \mathrm{ARB}
P
(
X
)
,
ARB
if and only if
A
⊂
B
\mathrm{A} \subset \mathrm{B}
A
⊂
B
. Is R an equivalence relation on
P
(
X
)
\mathrm{P}(\mathrm{X})
P
(
X
)
? Justify your answer.
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