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A relation R is defined from N to N as R...

A relation R is defined from `N` to `N` as R`={(ab,a+b): a,b in N}`. Is R a function from `N` to `N` ? Justify your answer.

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To determine whether the relation \( R = \{(ab, a+b) : a, b \in \mathbb{N}\} \) is a function from \( \mathbb{N} \) to \( \mathbb{N} \), we need to check if every element in the domain (which is \( \mathbb{N} \)) is related to a unique element in the codomain (also \( \mathbb{N} \)). ### Step-by-Step Solution: 1. **Understanding the Relation**: The relation \( R \) consists of pairs \( (ab, a+b) \) where \( ab \) is the product of two natural numbers \( a \) and \( b \), and \( a+b \) is their sum. 2. **Identifying the Domain and Codomain**: ...
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