# Relation and Function

## NCERT Exemplar Problem

### Short Answer Type

Question 1: Let A = {a, b, c} and the relation R be defined on A as follows:

R = {(a, a), (b, c), (a, b)}.

Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive.

**Solution:** In order to make R reflexive, (b, b) and (c, c) will be added to R.

And in order to make R transitive, (a, c) will be added to R.

Therefore, The minimum number of order pair to be added to R will be (b, b), (c, c) and (a, c) - Answer

Question 2: Let D be the domain of real valued function f defined by
then, write D.

**Solution:** Here given D is the domain of

Therefore,

Therefore, D = [– 5, 5] - Answer

Question 3:
be defined by
respectively. Then find g o f.

**Solution:**

Question 4:
be the function defined by

**Solution:**

Question 5: If A = {a, b, c, d} and the function f = {(a, b), (b, d), (c, a), (d, c)}, write f ^{– 1}

**Solution:** Given, f = {(a, b), (b, d), (c, a), (d, c)}

Therefore, f ^{– 1} ={(b, a), (d, b), (c, a), (c, d)} Answer

Question 6: If
is defined by

**Solution:** Given,

Question 7: Is g = {(1, 1), (2, 3, (3, 5), (4, 7)} a function? If g is described by g(x) = αx + β, then what value should be assigned to α and β?

**Solution:** Given, g = {(1, 1), (2, 3, (3, 5), (4, 7)}

Therefore, each of the element of domain will be have unique image.

Consequently, g is a function.

Now, after substituting the value of α in equation (i), we get