# Relation and Function

## NCERT Exemplar Problem

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 