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I'm trying to figure out the answer to this question and I think I have an answer, I just don t know if I'm right. Would you guys mind helping me out?

Let A = {a,b,c,d,e} and B = {a,e,i,o,u} and suppose f is a relation on A×B
given by f ={(a,i),(b,i),(c,a),(d,i),(e,e)}. Does the relation f define 
a function from A to B? What is the range of f ? Does the range equal the 
codomain?

I think that it is a function, because value of X maps to one value of Y. However, I'm having trouble finding the range. Would it simply be (i, e)?

Also, I know if the range equals the codomain then the function is considered onto. I think that this function is onto, but I'm not 100% sure.

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Yes, it is a function.

The range is the set $\{a, e, i\}$ which is clearly not equal to the co-domain, $B = \{a, e, i, o, u\}$.

So can the function be onto?

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  • $\begingroup$ Could you please explain why this is the range? $\endgroup$
    – Grant
    Apr 24, 2014 at 16:37
  • $\begingroup$ The range is the set of values to which elements of the domain are mapped. The first two elements in A are mapped to i, c is mapped to a, d to i, and e to e. So each element in A is mapped to one of the following: $\{a, e, i\}$, and no element in A is mapped to o or to u. $\endgroup$
    – amWhy
    Apr 24, 2014 at 16:40

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