Question

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question:
Q11 (a) Let R be the relation on the set N of natural numbers defined by
R = { (x,y) : x + 3y = 12 , x ∈ N, y ∈ N }.
(i) Express R and R
−1
in roster form

(ii) Find Domain of R
(iii) Find Domain of R
−1
(b) If f(x) = { a+bx, x 1
If lim
x→1
f(x) = f(1), what are the possible values of a and b ?

Answer 1

Let R be a relation defined on the set of natural numbers N as

R= {(x, y): x∈N,y∈N,2x+y=41}

Find the domain and range of this relation R. Also, verify whether R is (i) reflexive (ii) symmetric (iii) transitive.

ANSWER

Neither.

The relation R can be written as

R ={(1, 39), (2, 37), (3, 35), ........(10, 21).(11, 19), ..........(21, 1)}

∴ Domain of R = {1, 2, 3,..........19,20}

Range of R ={ 39, 37, 35,..........9, 7, 5, 3, 1}

For reflexive let's y=x so that 2x+x=41⇒ x=

3

41

but

R is not reflexive as x=

3

41

∈

/

N

R is not symmetric since ( 1, 39) ∈ R but ( 39, 1)∈

/

R.

R is not transitive because (20, 1) ∈ R and ( 1, 39) ∈ R but (20, 39) ∈

/

R.