Let $R$ be the relation on $\mathbb{N}$ defined by $R = \{(x, y): y = 2x, x, y \in \mathbb{N}\}$. Is $R$ a function?
AYes — every natural $x$ has exactly one image $2x$
BNo — multiple images
CNo — $R$ is empty
DOnly if $x$ is even
Answer & Solution
Correct answer: A. Yes — every natural $x$ has exactly one image $2x$
For every $x \in \mathbb{N}$, the rule $y = 2x$ assigns exactly one natural number $2x$. So $R$ is a function from $\mathbb{N}$ to $\mathbb{N}$. Its range is the even naturals.
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