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Following set is neither of even nor of odd so how can I express this by using set builder notation?

{0,3,6,9,12}

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2 Answers

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What you have there already is a form of set builder notation. If you’re asking how you can express it in set builder notation using some property or properties of the numbers in the set, notice that they are the multiples of $3$ between $0$ and $12$, inclusive:

$$\{0,3,6,9,12\}=\{n\in\Bbb N:n\le 12\text{ and }3\mid n\}\;,$$

where $3\mid n$ means that $n$ is a multiple of $3$, in case you’re not familiar with that notation. Another possibility is

$$\big\{3k:k\in\{0,1,2,3,4\}\big\}\;;$$

yet another is

$$\{n\in\Bbb N:\exists k\in\Bbb N(n=3k)\text{ and }n\le 12\}\;.$$

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You can also write it in this way: $\{\; 3x \;|\; x = 0, 1, 2, 3, 4 \;\}$.

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