# NCERT Class 11 Mathematics Solutions: Chapter 1 – Sets Miscellaneous Exercise Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. Let be the sets such that . Show

that .

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)

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.

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