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Byju's Answer
Standard XII
Mathematics
Number of Elements in a Cartesian Product
prove that if...
Question
prove that if A is a subset of B, B is a subset of C and C is a subset of A the A = C ?
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Solution
C
o
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l
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m
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t
a
∈
A
a
∈
A
S
i
n
c
e
A
⊂
B
a
∈
B
S
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n
c
e
B
⊂
C
a
∈
C
T
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r
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f
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,
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v
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y
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l
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m
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f
A
b
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l
o
n
g
s
t
o
C
A
⊂
C
_
_
_
_
_
_
_
_
_
_
1
C
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n
s
i
d
e
r
a
n
y
e
l
e
m
e
n
t
c
∈
C
c
∈
C
S
i
n
c
e
C
⊂
A
c
∈
A
T
h
e
r
e
f
o
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e
,
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v
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y
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f
C
b
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l
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n
g
s
t
o
A
C
⊂
A
_
_
_
_
_
_
_
_
_
_
_
2
F
r
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m
r
e
l
a
t
i
o
n
1
a
n
d
2
S
i
n
c
e
,
A
⊂
C
a
n
d
C
⊂
A
,
h
e
n
c
e
A
=
C
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0
Similar questions
Q.
If
A
is subset of
B
and
B
is a subset of
C
, then prove that
A
is subset of
C
.
Q.
For any two sets of A and B, prove that
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′
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′
if
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Q.
Show that if A is a subset of B then C-B is a subset of C-A
Q.
If set C is the super set of sets A and B and A
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