# Sets 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 **potato**

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.