Sets

Class Collins17th September

A B

u

Question 9 pg 16

(i) A∩C = {8,12} (ii) AUB = {0,1,2,3,4,5,8,9,12} (iii) B∩C = {8,9} (iv) AUC = {0,1,2,4,8,9,10,11,12} (v) BUC = {1,3,5,8,9,10,11,12} (vi) A∩B = {1,8}

Question 11 pg 16

(i) True (ii) False (iii) True (iv) True (v) False (vi) True (vii) True (viii) False (ix) True

Homework correctionHomework correction

Rules for listing elements of a set

(1) A capital letter is used to represent each set e.g. A, B, X, Y etc...

(2) Elements are listed within curly brackets e.g. {……..}

(3) A comma is used between each element e.g. {1,2,3,4,5}

(4) Elements are NEVER REPEATED

(5) The order of the elements is not important e.g. {b, c, g, f, a, d}

Sets RevisionSets Revision

UnionAll of the elements in A and B

Set Revision

A5

BABA

BA

#(A)

u

IntersectionThe elements that are common to both A and B

‘Element of’5 is an element of set A

A4 ‘Not an Element of’4 is not an element of set A

‘Subset of’A is a subset of B – Every element of set A is in set B

BA ‘Not a Subset of’A is not a subset of B

The null setA set that contains no elements

The cardinal numberThe number of elements in set A The universal setThe set containing all the elements used in the question – Big rectangle is used to represent it

Or { }

BA Equal SetsSets are said to be equal if ALL elements of A are also in B

A Bu

Example: u = {a,b,c,d,e,f,g,h,i}

A = {a,b,c,d,e}

B = {c,e,f,h}

Represent u, A and B with a Venn Diagram

Venn Diagram QuestionsVenn Diagram Questions

a.

d.

e.

c.

h.

f.

b.

g.

i.

Find:

(i) A∩B

(ii) AUB

(iii) # A

(iv) # B

(v) # (A∩B)

(vi) # (AUB)

={c,e}

= {a,b,c,d,e,f,h)

= 5

= 4

= 2

= 2

A B u

Example: u = {a,b,c,d,e,f,g,h,i}

A = {a, c, e, i}

B = {e, f, g, h, i}

Represent u, A and B with a Venn Diagram

.a

.c .e

.i

h.

f.

g.

.d

List the elements of:

(i) A'

(ii) B'

(iii) (AUB)'

(iv) (A∩B)'

= {b,d,f,g,h}

= {b,d,f,a,c}

= {b,d}

= {b,d,a,c,f,g,h}

Complement of a Set Complement of a Set Complement of set A means all the elements in the universal set except for the elements in set A

We use the symbol A' to represent the complement of a set

To find A’ simply cover the entire set of A and list the rest of the elements

.b

Class Work Question 3 pg 19 Any questions, ask Mr. Bruton

Question 2 pg 18 Question 7 pg 19

Home Work