# NCERT Class 11 Mathematics Solutions: Chapter 1 – Sets Miscellaneous Exercise Part 4

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1. Show that for any sets and ,

Answer:

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) .

Answer: (i)

To show:

We know that

………….. eq(1)

Also, ………………. eq (2)

∴ From (1) and (2),

Answer: (ii)

To show:

{from (1)}