Question

Example 8. Let relation R defined on the set of natural numbers N be as follows, R= [(x, y):x€N, N, 2x + y = 41}. Find the domain and range of the relation R, Also verify whether R is reflexive, symmetric and transitive. So R​

Answer 1

Step-by-step explanation:

hlo mate here's your 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.

I hope its help you mark as brainlist