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Byju's Answer
Standard XII
Mathematics
De Morgan's Law
If A × B ⊆ C ...
Question
If A × B ⊆ C × D and A × B ≠ ϕ, prove that A ⊆ C and B ⊆ D.
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Solution
Let
:
(
x
,
y
)
∈
(
A
×
B
)
∴
x
∈
A
,
y
∈
B
Now
,
∵
(
A
×
B
)
⊆
(
C
×
D
)
∴
(
x
,
y
)
∈
(
C
×
D
)
Or
,
x
∈
C
a
n
d
y
∈
D
Thus
,
we
have
:
A
⊆
C
&
B
⊆
D
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