by user634631
Last Updated June 30, 2020 04:20 AM

confused about the answer from the given options. In mapping every element of domain has exactly one image. But the given options do not make any sense. What will be the answer? I think none of them. Am i right?

$f$ is a function if and only if to every element $a$ of $A$ is associated a unique element $f(a)$ of $B$, hence none of them.

Lets look at this answer by answer.

(a) $f$ is a mapping only if it is is one to one (injective). This is not true, becuase we know mappings exist that are not injective. Look at $f:\mathbb N\to\mathbb N$ where $f(x) = 1$ This is clearly not injective but is a mapping. (write out a proof for this if this is not immediately clear)

(b) Take the same $f$ as above, we know this is map, but it is clearly not onto (surjective) because it only maps to 1. (write out a proof for this if this is not immediately clear)

(c) The same reasoning above applies here

(d) the answer must be d.

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