Let f be the subset of `Z xxZ` defined by `f" "=" "{(a b ," "a" "+" "b)" ":" "a ," "b in Z}` . Is f a function from Z to Z? Justify your answer.

Explanation

The relation f is defined as
`f={(ab,a+b):a,binZ}`

We know that a relation f from set A to set B is said to be a function if every element of set A has unique images in set B.

Since `2,6inZ`,

`⇒(2xx6,2+6)inf`

Again since,` −2,−6inZ,

⇒(−2xx−6,−2+(−6))inf`

i.e., `(12,8),(12,−8)inf`

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