When defining sets, there are several important concepts to be aware of.

Consider A = {banana, squash, watermelon, corn, pepper, peach, tomato, strawberry}, the set of all food shown in the picture. Although there are multiple bananas, peaches, and strawberries, each item is listed only once in the set. This applies to all sets. Elements are not repeated when a set is written using the roster method.



The set of round purple fruit is an empty set because no round purple fruit are in the picture, which means no elements are available to put into this set. You write the empty set as { } or .

Sets are unordered. So sets that contain the same elements are considered equal even if the elements are written in a different order.


Q ={pepper, tomato, strawberry} and
Z = {tomato, pepper, strawberry} are equal.


The set of round red food is S = {tomato}. Because only one food fits the description of round red, S has only one element, and S is called a singleton. The set of oval green food G = {watermelon} also has only one element and is a singleton. Because S and G have the same number of elements, you say they are equivalent.