# NCERT Class 11 Mathematics Solutions: Chapter 1 – Sets Miscellaneous Exercise Part 4 (For CBSE, ICSE, IAS, NET, NRA 2023)

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1. Show that for any sets and ,

To show:

Let

We have to show that

Case I:

Then,

Case II:

… eq (1)

It is clear that

… eq (2)

From (1) and (2) , we obtain

To prove:

Consider

… eq (3)

Next, we show that .

… eq (4)

Hence, from (3) and (4) ,

We obtain

2. Using properties of sets show that

(i)

(ii) .

To show:

We know that

… eq (1)

Also, … eq (2)

∴ From (1) and (2) ,