Let N denote the set of all natural numbers. Define two binary relations on N as R_{1} = {(x,y) in N X N:2x + y = 10} and R_{2} = {(x,y) in N X N:x + 2y = 10}. Then:: Relation (Mathematics)

Let

N

denote the set of all natural numbers. Define two binary relations on

N

as\\

R_{1} = \{(x,y) \in N \times N:2x + y = 10\}

and

R_{2} = \{(x,y) \in N \times N:x + 2y = 10\}

. Then:

Both

R_{1}

and

R_{2}

are symmetric relations\\

Range of

R_{1}

\{ 2,4,8\}

Both

R_{1}

and

R_{2}

are transitive relations\\

Range of

R_{2}

\{ 1,2,3,4\}

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