Q.Describe the following set in Set-Builder form: $\left\{\dfrac{1}{2}, \dfrac{2}{5}, \dfrac{3}{10}, \dfrac{4}{17}, \dfrac{5}{26}, \dfrac{6}{37}, \dfrac{7}{50}\right\}$.

A set is a collection of well-defined objects — a collection where it is always possible to say for certain whether any given object belongs to it or not (this rules out vague groupings like 'clever students', where different people would disagree on membership). A set can be described in three standard ways. The Roster (or Tabular/List) method writes out every element explicitly inside braces, separated by commas, e.g. {Monday, Tuesday, ..., Sunday}; repeated elements are listed only once, and the order of listing does not matter. The Set-Builder (or Rule) method instead states the defining property that every element must satisfy, in the form {x / property of x}, e.g. {x / x is a month of the year}; this is especially useful when a set is too large, or impossible, to list out completely. The Venn diagram method represents a set pictorially, using a closed curve (circle, triangle, rectangle, or any closed shape) with the elements shown as points inside it — this is particularly useful for …