Polygon ABCD is translated to create polygon A'B'C'D'. Point A is located at (1,5), and point A' is located at (-2,1). What is t
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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.