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Let $f$ be the subset of $Z \times Z$ defined by $f=\{(a b, a+b)$ : $a, b \in Z\}$. Is $f$ a function from $Z$ to $Z$ ? Justify your answer.
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Let $a=0, b=1, \therefore a b=0, a+b=1,(0,1) \in f$ $a=0, b=2, \quad \therefore a b=0, a+b=2,(0,2) \in f$
$\therefore$ For the same element there are different images.
$\therefore f$ is not a function.
$\therefore$ For the same element there are different images.
$\therefore f$ is not a function.
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