Manipulating Sets

Manipulating Sets

GCSE(F) GCSE(H)

Sets can be joined together: `O uu P` is read as O union P, and lists each element if it is set O OR if it is in set P. Elements in both sets are only listed once:

`O = {1, 3, 5, 7, 9, 11}`

`P = {2, 3, 5, 7, 11}`

`O uu P = {1, 2, 3, 5, 7, 9, 11}`

Elements that are in both two sets can be identified using an intersect, which is shown with the `nn` symbol. Using the same sets: `O nn P = {3, 5, 7, 11}` which lists all the elements that are in set O AND in set P.

These techniques are not limited to two sets of data. To manipulate three sets of data, work out the elements for two sets; then, using that answer, repeat the technique for the third set.

Examples

1. The number cards in one suit of a set of playing cards are defined as a universal set, such that `xi = {2, 3, 4, 5, 6, 7, 8, 9 and 10}`.

Set E contains all the even numbers. Set T contains all the numbers that are a multiple of 3. List the elements in `E nn T`.

Answer: `E nn T = {6}`

`E = {2, 4, 6, 8, 10}` `T = {3, 6, 9}` `E nn T ` is E intersection T: values have to be in both sets `E nn T = {6}`

2. 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`.

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

`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}`

`T = {3, 6, 9}`

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