NCERT Class 11-Math՚s Exemplar Chapter 1 Sets CBSE Board Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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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,