Prove De Morgan's law by showing that each side is a subset of the other side by considering x ∈ A⎯⎯⎯ A ¯ ∩ B⎯⎯⎯ B ¯ .
1 answer:
Solution :
We have to prove that
(De-Morgan's law)
Let
then
and 
and so
and
.
Thus,
and so 
Hence,
.........(1)
Now we will show that 
Let
⇒
Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.
and 
Therefore,
and we have
.............(2)
From (1) and (2),
Hence proved.
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