NCERT Class 11-Math's Exemplar Chapter 1 Sets CBSE Board Problems
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Question 3:
If X and Y are subsets of the universal set U, then show that
(i)
(ii)
(iii)
Answer:
(i)
(ii)
(iii) Note that
Hence the result follows.
Example 4:
Given that , then
(i) Write the subset A of N, whose element are odd numbers.
(ii) Write the subset B of N, whose element are represented by , where.
Answer:
(i)
(ii)
So, for
and so on. Therefore,
Question 5:
Given that . If represents any member of E, then, write the following sets containing all numbers represented by
(i)
(ii)
Answer:
Given
(i) Let
Thus, for
and so on. Therefore, .
(ii) Let
So, for
and so on. Hence,
Question 6:
Let . If n represent any member of X, express the following as sets:
(i)
(ii)
(iii) is greater than .
Answer:
For , it is the given that , but .
Let,
Now, as
But
So,
Let
Here,
as and and there is no other element belonging to X such that .
(iii)
Let
Therefore,