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Byju's Answer
Standard XII
Mathematics
De Morgan's Laws
If A, B and C...
Question
If A, B and C are any three sets, then
A
−
(
B
∪
C
)
is equal to
A
(
A
−
B
)
∪
(
A
−
C
)
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B
(
A
−
B
)
∩
(
A
−
C
)
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C
(
A
−
B
)
∪
C
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D
(
A
−
B
)
∩
C
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Solution
The correct option is
B
(
A
−
B
)
∩
(
A
−
C
)
U
−
(
P
∪
Q
)
=
(
P
∪
Q
)
c
(
P
∪
Q
)
c
=
P
c
∩
Q
c
=
(
U
−
P
)
∩
(
U
−
Q
)
It is De' Morgan law.
Now, just replace U with A, P with B and Q with C.
We will get,
A
−
(
B
∪
C
)
=
(
A
−
B
)
∩
(
A
−
C
)
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If A, B and C are any three sets, then
A
×
(
B
∩
C
)
is equal to
Q.
For any three sets A, B and C, (A ∪ B ∪ C) ∩ (A ∩ B' ∩ C') ∩ C' is equal to ____________.