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I need to write following set in to set builder notation.

$\{ 0,3,6,9,12 \}$

Solution which I found on internet is:

$\{3x\;|\;\text{where }x\text{ is an integer and }0\leq x \leq 4\}$

What I thought is :

$\{x\;|\;x\text{ is multiple of }3\text{ and }0\leq x \leq 12\}$

Now which one is correct? or none of the above?

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    $\begingroup$ I think you mean $\{x \mid x \text{ is a multiple of 3 and }0\leq x \leq 12\}$? If this is the case, then both are correct. $\endgroup$ – D. N. Apr 4 '14 at 4:46
  • $\begingroup$ yes that is mistake,going to update $\endgroup$ – user3461957 Apr 4 '14 at 4:47
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    $\begingroup$ $ \{ x : x \in \{ 0, 3, 6, 9, 12 \} \} $ $\endgroup$ – Justus87 Apr 4 '14 at 10:39
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Both are correct: there are all sorts of ways to answer this question. Here are a few more.

  • $\{x\mid x=0\text{ or }x=3\text{ or }x=6\text{ or }x=9\text{ or }x=12\}$.
  • $\{6+3x\mid x\in\mathbb Z\text{ and }-2\leq x\leq2\}$.
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Both are correct. In general, there are many different ways to express the same set using set builder notation.

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