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

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Understanding the different types of sets

Understanding the Different Types of Sets

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.