NCERT Class 11 Mathematics Solutions: Chapter 1 – Sets Miscellaneous Exercise Part 1
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Understanding the Different Types of Sets
1. Decide, among the following sets, which sets are subsets of one and another:
Answer:
Here, are the only solutions of .
Hence,
2. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
(i) If and , then
(ii) If and , then
(iii) If and , then
(iv) If and , then
(v) If and , then
(vi) If and , then
Answer: (i) - False
Let
Now,
However,
Answer: (ii) - False
Let
And
But, .
Hence, statement is false.
Answer: (iii) - True
Let, .
Consider, it is given that ,
it is given that , so that
Hence .
Answer: (iv) – False
Consider
In above example
Hence given statement is false.
Answer: (v) – False
Consider
In above example if
.
Hence given statement is false.
Answer: (vi) – True
Consider so that all element of set will belongs to set .
If set don’t have element then cannot have this element.