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

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Question 6:

If A and B are subsets of the universal set U, then show that

(i)

(ii)

(iii)

Answer:

(i) Given: A and B are two subsets

To prove:

Let

Hence Proved

(ii) Given: A and B are two sets

To prove:

Let

We know,

From (1) and (2) :

Now,

Let

So,

Hence Proved

(iii) Given: A and B are two subsets

To prove:

Let

and

Hence Proved

Question 7:

Given that . Then write

(i) The subset of N whose elements are even numbers.

(ii) The subset of N whose element are perfect square numbers.

Answer:

(i)

(ii)

Question 8:

If , if n represents any member of X, write the following sets containing all numbers represented by

(i)

(ii)

(iii)

(iv)

Answer:

(i)

(ii)

(iii)

(iv)

Question 9:

If , and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

(i)

(ii)

(iii)

Answer:

(i)

(ii)

(iii)

Question 10:

A, B and C are subsets of Universal Set U. If

and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.

Answer:

Venn Diagram