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

To determine whether the set \( f = \{(ab, a + b) : a, b \in \mathbb{Z}\} \) is a function from \( \mathbb{Z} \) to \( \mathbb{Z} \), we need to analyze the definition of a function. A relation \( f \) is a function if for every element \( x \) in the domain, there is exactly one element \( y \) in the codomain such that \( (x, y) \) is in the relation.

### Step-by-Step Solution:

1. **Identify the elements of the set \( f \)**:
The set \( f \) consists of pairs \( (ab, a + b) \) where \( a \) and \( b \) are integers. Here, \( ab \) represents the product of \( a \) and \( b \), and \( a + b \) represents their sum.

2. **Choose specific values for \( a \) and \( b \)**:
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