A **set** is a collection of objects. The objects are called **elements** or **members**. We usually use capital letters to name sets and list the elements in braces.

**Examples**

**1**. A = {a, b, c, d, e, f} is a list containing the first six letters of the alphabet.

**2**. B = {1, 2, 3, 4 … 20} is a set containing the counting numbers 1 through 20.

The **empty set** (or **null set**) is a set with no members or elements at all. It is represented by the symbol:** { } **or** Ø**.

*It would incorrect to write the empty or null set as *{Ø}*, as the set* {Ø}* contains one element*.

The symbol ∈ is used to mean ** is an element of**, and the symbol ∉ is used to mean

**.**

*is not an element of*If C = {orange, pineapple, banana}, we can say that banana C, but mango C.

Sometimes we don’t list the members of the set, we use a notation called **set-builder notation**.

The expression **{ x | x is a vowel}** describes the “set of all

**x**such that

**x**is a vowel”. The bar,

**|**, is read “

*such that*”.