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NCERT Class 11 Mathematics Solutions: Chapter 1 β Sets Miscellaneous Exercise Part 4
1. Show that for any sets and ,
Answer:
To show:
Let
We have to show that
Case I:
Then,
Case II:
β¦ eq (1)
It is clear that
β¦ eq (2)
From (1) and (2) , we obtain
To prove:
Consider
β¦ eq (3)
Next, we show that .
β¦ 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
β¦ eq (1)
Also, β¦ eq (2)
β΄ From (1) and (2) ,
Answer: (ii)
To show:
{from (1) }