Representation of Sets

Sets are abstract collections, but to work with them we need a concrete way to write them down. The most direct method is the roster or tabular form, where we simply list every element inside curly braces — for example, the set of vowels is $\{a, e, i, o, u\}$. When the pattern is clear but the list would be endless, we use the set-builder form, which describes the common property that all elements share: $\{x : x \text{ is a vowel in English}\}$. Mastering both represe …