NCERT Class 11 Mathematics Solutions: Chapter 1 –Sets Miscellaneous Exercise Part 2

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In figure definitions of the union and intersection are given.

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.