NCERT Class 11 Mathematics Solutions: Chapter 1 – Sets Miscellaneous Exercise Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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.