NCERT Class 11 Mathematics Solutions: Chapter 1 –Sets Miscellaneous Exercise Part 2
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Definition of Union and Intersection
In figure definitions of the union and intersection are given.
1. Let be the sets such that . Show
that .
Answer:
Consider
There can be two cases,
Case-1
As and so that
Given that , so that
then so that .
Case-2,
We have already assumed that .
Hence,
Given that , so that
But we assumed that . Hence
then so that .
So in both cases ...(1)
Similarly, we can prove ...(2)
From equation (1) and (2)
2. Show that the following four conditions are equivalent:
(i)
(ii)
(iii)
(iv)
Answer:
First, we shall try to prove
Given
To prove
so that
Given
To prove
Let
Given that
So all element of must be in Set B
So,
That
So, proved
Similarly you can solve all other parts.