NCERT Class 11 Mathematics Solutions: Chapter 1 – Sets Miscellaneous Exercise Part 4
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Set Operations: Intersection
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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)}