Question

consider the relation R defined by R={(x,y):y=2x-3,x,y€N},Is R a function on N ?Why?​

Answer 1

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.