EnglishSets and functionsSubsets
The idea of set equality can be broken down into two separate relations: two sets are equal if the first set contains all the elements of
Definition (Subset)
Suppose and are sets. If every element of is also an element of , then we say is a subset of , denoted .
If we visualize a set as a
Here has
Two sets are equal if
The relationship between "
Exercise
Think of four pairs of real-world sets which satisfy a subset relationship. For example, the set of cars is a subset of the set of vehicles.
Exercise
Suppose that is the set of even positive integers and that is the set of positive integers which are one more than an odd integer. Then
Solution. We have , since the statement " is a positive even integer"
Likewise, we have , because " is one more than an positive odd integer"
Finally, we have , since
Exercise
Drag the items below to put the sets in order so that each set is a subset of the one below it.
