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Let R be a relation on the set of natura...

Let R be a relation on the set of natural numbers N, defined as:
`R={(x,y):y=2x,x,y in N}.`
Is R a function from `N xxN`? If yes find the domain, co-domain and range of R.

Text Solution

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The correct Answer is:
N/a
`because` For each `x in N, 2x in N` is unique.
`because` For each `x in N `, x has one and only one image.
`therefore ` R is a function from N to N.
Domain of R =set of natural numbers N
Co-domain of R=set of natural numbers N. (Co-domain is the total elements of which Range is the subset)
Range of `R={2x: x in N}`.
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