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}