3 ∈ {odd numbers} means that 3 *is an element of* the set of odd numbers.

2 ∉ {odd numbers} means that 2 does not belong to that set.

A **subset** is a set where elements in the subset are part of another set. A subset cannot include elements that are not in the original set.

If only *some* of the elements of a subset appear in the original set, then that is called a **proper subset**, and will have fewer elements than the original set. A proper subset is shown as D ⊂ E, where D is a proper subset of E. If it is not a proper subset, then the symbol has a diagonal line through it.

A subset of data that matches the original set is shown as B ⊆ A (B is a subset of *or equal to* A).

Set P^{c} (sometimes P` ) are all the elements that are not in P: this is the **complement** of set P.

An empty set is shown with the sign ∅, and represents the set { }.

The number cards in a suit of playing cards are defined as the universal set, so

`xi = {2, 3, 4, 5, 6, 7, 8, 9 and 10}`.

If E contains the set of even numbers, write the members of E^{c}.

The complement of E is required: those elements that are not in E. Use a small ^{c} to show it is a complement.

Answer: E^{c} = {3, 5, 7, 9}

Number cards in a single suit of playing cards are defined as the universal set:

`xi = {2, 3, 4, 5, 6, 7, 8, 9 and 10}`.

If E contains the set of even numbers, and T contains the set of numbers that are a multiple of 3, write the set for `E^c uu T`.

`E = {2, 4, 6, 8, 10}`

The complement of E is required, elements in the universal set that are not in E:

`E^c = {3, 5, 7, 9}` and `T = {3, 6, 9}`

The union is required, elements in both lists: `E^c uu T = {3, 5, 6, 7, 9}`

Answer: `E^c uu T = {3, 5, 6, 7, 9}`

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