Let `A` be the set of two positive integers. Let `f: AvecZ^+` (set of positive integers) be defined by `f(n)=p ,` where `p` is the highest prime factor of `n` . If range of `f={3}dot` Find set `Adot` Is `A` uniquely determined?

Answer

N/a

Explanation

Let A ={n,m} where n and m are positive integers.
`therefore f(n)=f(m)=3`
`implies` Largest prime factor of n and m =3
`implies m=3, m=6, or n=3, m=9 or n=3, m=12, or n=6, m=9,…..`
`implies A={3,6}` or {3,9} or {3,12} or {6,9} , etc.
`therefore ` A cannot be unique.