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Let $X$ be the set $\{1, 2, 3, 4, 5\}$ and $Y$ be the set $\{6, 7, 8, 9, 10\}$. We describe the functions $f : X\rightarrow Y$ and $g : X\rightarrow Y$ in the following tables. Answer each part and give a reason for each negative answer.

 

$n$ $f(n)$
1 6
2 7
3 6
4 7
5 6

 

$n$ $g(n)$
1 10
2 9
3 8
4 7
5 6

 

  1. Is $f$ one-to-one?
  2. Is $f$ onto?
  3. Is $f$ a correspondence?
  4. Is $g$ one-to-one?
  5. Is $g$ onto?
  6. Is $g$ a correspondence?
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