# NCERT Class 11 Mathematics Solutions: Chapter 2 –Relations and Functions Miscellaneous Exercise Part 3

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1. Let be a function from to defined by , for some integers . Determine.

Answer:

On substituting in

We obtain.

So, the respective values of are .

2. Let be a relation from defined by . Are the following true?

(i) , for all

(ii) , implies

(iii) implies .

Justify your answer in each case.

Answer:

Answer:(i)

It can be seen that ; however, .

Therefore, the statement “” is not true.

Answer:(ii)

It can be seen that because and .

Now, ; therefore,

Therefore, the statement is not true.

Answer:(iii)

It can be seen that because and .

Now, ; therefore,

So, the statement is not true.

3. Let . Are the following true?

(i) is a relation from

(ii) is a function from . Justify your answer in each case.

Answer:

It is given that

Answer:(i)

A relation from a non-empty set to a non-empty set is a subset of the Cartesian product .

It is observed that f is a subset of .

is a relation from .

Answer: (ii)

Since the same first element i.e., corresponds to two different images i.e., , relation is not a function.