Set Builder Notation

[Pages:5]Set Builder Notation:

Grade 9 Sets of Numbers and Cardinality Cardinal Number or Cardinality: The number of distinct elements in a set. n(A): n of A; represents the cardinal number of a set. K = {2, 4, 8, 16} ---------- n(K) = 4 R = {1, 2, 3, 2, 4, 5} --------- n(R) = 5 P = {} --------- n(P) = 1

Universal set: the set that contains every object of interest in the universe. Complement of a Set: A set of objects of the universal set that are not an element of a set inside the universal set. Notation: A - means not a member of set A. If E = { l, m, n, o, p, q, r, s, t } and A = { n, p, s, t } then A = { l, m, o, q, r } A are those members of the universal set that are not in set A. Venn Diagram: A rectangle represents the universal set and circles represent sets of interest within the universal set

Subset of a Set: Set A is a Subset of B if every element of A is an element of B. Notation: A B A {3, 4, 5, 6} B {3, 4, 5, 6, 8} BB Note: Every set is a subset of itself. The empty set is a subset of every set, because every element of the empty set is an element of every other set. { } or Number of Subsets The number of subsets of a set with n elements is: 2n List the subsets and proper subsets {1, 2} Subsets: {1} {2} {1,2} ; 22 = 4 If A is a subset of B we write A B to designate that relationship. If A is a proper subset of B we write

A B to designate that relationship. The set A = {1, 2, 3} is a subset of the set B ={1, 2, 3, 4, 5, 6} because each element of A is an element of B.

If A is not a subset of B we write A B to designate that relationship. The set A = {3, 5, 7} is not a subset of the set B = {1, 4, 5, 7, 9} because 3 is an element of A but is not an element of B.

Grade 9

MATHEMATICS SETS WORKSHEET

1. If Y = 5, 1, 4, 1, 2, 6, 1 , then n(Y) =

2. If S = a,b,c,b,e, f ,b,e, f , then n(S) =

3. Find the n(X), when X= {5, 5, 6, 6, 7} 4. List the elements of Set A, when A= {multiples of 5 up to 30}

5. Given that B = { a, b, c, d }; state n (B) 6. D = { 2, 3, 5, 7, 11, 13 } ; How many subsets does D have?

7. If A = { f, g, h, i } ; write the subsets of A.

8. If U = { 3, 5, 7, 9, 11 } and A = {3, 7, 11 } ; What is A? 9. E = { even numbers no more than 10 } and P = { 2, 4 } ; State the elements of P.

10. If P ={3, 4, 5, 6} and Q = {3, 5, 7, 9}, then Q P is? 11. X = { 1, 3, 5, 7, 8 } and Y = { 1, 4, 6, 8}; What is X U Y ? 12. U = { 1, 2, 3, 4, 5, 6, 7, 8, 9} , A = { 1, 3, 5, 7, 8 } and B = { 1, 4, 6, 8 } List the elements of:

i.

A

ii. A B

iii. A U B

13. Given the following information: U = {3, 6, 9, 12, ..., 27} E = {even numbers} G = {numbers greater than 20} E and G are subsets of U i. List the members of E and of G

ii. Draw a Venn diagram to represent the above data

14. Draw a venn diagram to represent the information; M = { even number less than 10 } N = { odd number greater than 10 but less than 20 }

15. Draw a Venn diagram to represent the sets below; E = { 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } Q = { 4, 8, 12 } P = { 3, 6, 9, 12 }

Read the story about " The Hernandez Family", then do the activities that follows. Mr and Mrs Hernandez have three children, two girls and one boy. Their names are Jada, Jasmine and Justin. They all love to watch television, so Mr Hernandez sets aside Sunday afternoon for them to do so. While watching TV, they eat their favourite snack of carrot sticks and bean dip. They used to have buttery popcorn as their snack during TV time but Justin disliked it. He is happy that they now have carrot sticks instead. Mrs Hernandez is happy too. She Justin and Jasmine are vegetarians and the carrot is a healthy snack for them. All the family members have similar interests. They all like to watch Comedy Hour, Nightly News Sports Watch and The Road to Success. All these television programmes are aired on Sunday between the hours of 4:00 p.m and 7:30 p.m.

16. Create at least four sets from the story.

17. List the members of the set of children who watch Nightly News on a Sunday in the Hernandez family. Then write the name of another set that the same children could be apart of.

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