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 Pc (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 Ec.
The complement of E is required: those elements that are not in E. Use a small c to show it is a complement.
Answer: Ec = {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}`