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Question

Let R be a relation in N defined as R={(x,y)N×N:x+2y=39} Find the domain, co-domain and range of R. Also write R1 in roster form.

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Solution

x+2y=39

y=39x2

Since yN,y>0

39x2>0

39x>0

x<39

Since xN,x can take values ={1,2,....38}

Domain of R ={1,2,....38}

Range of R is y=39x2,forx={1,2,....38}

Range of R ={1,2,....,37}

when x=1,y=19

when x=2,y=18.5

when x=37,y=1

Domain of f ={1,2,....38}

Range of f ={1,2,....37}

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