If $f:N ightarrow Z$ is defined by $f(n) = \left\{ \begin{array}{r} 2\ \ \ if\ \ \ n\ = \ 3k,\ k \in Z \ 10\ \ if\ n = 3k + 1,\ k \in Z, \ 0\ if\ n = 3k + 2,\ k \in Z \end{array} ight.\$ Then $\{ n \in N:f(n) 2\}$ is equal to

Question

If $f:N ightarrow Z$ is defined by $f(n) = \left\{ \begin{array}{r} 2\ \ \ if\ \ \ n\ = \ 3k,\ k \in Z \ 10\ \ if\ n = 3k + 1,\ k \in Z, \ 0\ if\ n = 3k + 2,\ k \in Z \end{array} ight.\$ Then $\{ n \in N:f(n) > 2\}$ is equal to

Dr. Abubacker · Accepted Answer

(b)
We have
$f(n) = \left\{ \begin{array}{r}
2\ \ \ if\ \ \ n = 3k,\ \ k \in Z \
10\ \ \ \ \ if\ \ \ \ \ \ n = 3k + 1,\ k \in Z \
0\ \ \ if\ \ \ \ n = 3k + 2,\ \ k \in Z
\end{array} ight.\$
For $f(n) > 2$, we take $n = 3k + 1,\ k \in Z$
$\Rightarrow \ \ \ \ n = 1,\ 4,\ 7$
$	herefore$ Required set $\left\{ n \in Z;f(n) > 2 ight\} = \{ 1,\ 4,\ 7\}$

Q. If $f:N \rightarrow Z$ is defined by $f(n) = \left\{ \begin{array}{r} 2\ \ \ if\ \ \ n\ = \ 3k,\ k \in Z \\ 10\ \ if\ n = 3k + 1,\ k \in Z, \\ 0\ if\ n = 3k + 2,\ k \in Z \end{array} \right.\$ Then $\{ n \in N:f(n) > 2\}$ is equal to

Explanation

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