Which set builder notation describes $\left\{ { - 2, - 1,0,1,1,2,3,4,5,6} \right\}$ ?
A. $\left\{ {x{\text{| - 2}} \leqslant {\text{x}} \leqslant 6{\text{ where x is an integer}}} \right\}$
B. $\left\{ {x{\text{| - 2 < x < }}6{\text{ where x is an integer}}} \right\}$
C. $\left\{ {x{\text{| - 2 < x}} \leqslant 6{\text{ where x is an integer}}} \right\}$
D. $\left\{ {x{\text{| - 2}} \leqslant {\text{x < }}6{\text{ where x is an integer}}} \right\}$
E. None of the above

Hint: Set builder notation is used to describe or define the elements present in a set or to state the properties that its member elements must satisfy. Here the element is all integers as they include both negative and positive numbers.

Complete step by step solution: We have to find the set notation for set $\left\{ { - 2, - 1,0,1,1,2,3,4,5,6} \right\}$
We can find the set notation by solving the given options.
In A, it says that x is such an element which is greater than or equal to $ - 2$ but less than or equal to $6$ which means it includes all the numbers from $ - 2$ to $6$, then the set is-
x=$\left\{ { - 2, - 1,0,1,1,2,3,4,5,6} \right\}$
In B, it says that x is such an element which is greater than $ - 2$ but less than $6$ which means it includes the numbers from $ - 1$ to \[5\], then the set is-
x=$\left\{ { - 1,0,1,1,2,3,4,5} \right\}$
In C it says that the x is such an element which is greater than $ - 2$and less than or equal to $6$which means the numbers are from $ - 1$to$6$, then the set becomes-
x=$\left\{ { - 1,0,1,1,2,3,4,5,6} \right\}$
In D it says that x is such an element which is greater than or equal to $ - 2$ but less than$6$which means it includes all the numbers from $ - 2$ to\[5\]
x=\[\left\{ { - 2, - 1,0,1,1,2,3,4,5} \right\}\]

Hence the correct answer is A.

Note: Note: Set builder notation is used to write sets with an infinite number of elements in shorthand. We can describe all types of the number using this notation. It is used in –
1) Computer science for programming languages like Python and Haskell.
2) Inset theories to describe complex expressions.
3) In mathematical logic.