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Question:
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If $f: N \rightarrow Z$ is defined by
$$
f(n)=\left\{\begin{array}{l}
2 \text { if } n=3 k, k \in Z \\
10 \text { if } n=3 k+1, k \in Z \\
0 \text { if } n=3 k+2, k \in Z
\end{array}\right.
$$
Then , $\{n \in N: f(n)>2\}$ is equal to
Options:
$$
f(n)=\left\{\begin{array}{l}
2 \text { if } n=3 k, k \in Z \\
10 \text { if } n=3 k+1, k \in Z \\
0 \text { if } n=3 k+2, k \in Z
\end{array}\right.
$$
Then , $\{n \in N: f(n)>2\}$ is equal to
Solution:
1386 Upvotes
Verified Answer
The correct answer is:
$\{1,4,7\}$
We have,
$$
f(n)= \begin{cases}2 & \text { if } n=3 k, k \in Z \\ 10 & \text { if } n=3 k+1, k \in Z \\ 0 & \text { if } n=3 k+2, k \in Z\end{cases}
$$
For $f(n)>2$, we take $n=3 k+1, k \in Z$
$$
\begin{aligned}
& \Rightarrow \quad n=1,4,7 \\
& \therefore \text { Required set }\{n \in Z ; f(n)>2\} \\
& =\{1,4,7\} \\
&
\end{aligned}
$$
$$
f(n)= \begin{cases}2 & \text { if } n=3 k, k \in Z \\ 10 & \text { if } n=3 k+1, k \in Z \\ 0 & \text { if } n=3 k+2, k \in Z\end{cases}
$$
For $f(n)>2$, we take $n=3 k+1, k \in Z$
$$
\begin{aligned}
& \Rightarrow \quad n=1,4,7 \\
& \therefore \text { Required set }\{n \in Z ; f(n)>2\} \\
& =\{1,4,7\} \\
&
\end{aligned}
$$
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