Operations on sets

OPERATIONS ON SETSby: Teacher MYRA CONCEPCION

UNDERSTANDING

UNIVERSAL SETS…A B C D E F G

H I J K L M N O P Q

R S T U V W

X Y Z

…-5 -4 -3 -2

-1 0 1 23 4 5

36 7 8 9

10 11 12 13 14 15 …

A = {f,r,e,s,h,m,a,n}B = {1,4,3}

UNIVERSAL SET is where all the sets belong.

In other words, all sets are a subset of Universal Set.

REMEMBER: U is the symbol for universal set!

If a set consists of elements such as Philippines, Korea, United States

and France, what could be the universal set?

The universal

set is consist of

COUNTRIES!

UNDERSTANDING

COMPLEMENTS OF A SET…

c r u s h

U

A A = {c,r,u,s,h} orA = {x|x is a letter in the word “crush”}

A’={a,b,d,e,f,g,i,j,k,l,m,n,o,p,q,t,v,w,x,y,z}

COMPLEMENT OF A SET is a set of elements that can be found in U but not in a certain set. It

is denoted by ’.In other words,

complements of a set are elements that are

OUT OF PLACE!

FYI: There is another symbol for complement of a

set!

If a set consists of letters in the sentence “The quick brown fox jumps over the lazy dog.”, what could be its complement to U?

There will be no

complement! The sentence

consists all the letters of the

English alphabet.

UNDERSTANDING

COMPLEMENTS OF A SET…

A = {1,2,4,5,7} B = {1,3,5,6}A – B

The complement of B with respect to A.

= {2,4,7}

B – A The complement of A with respect to B.

= {3,6}

What is F – B ifF = {t,e,a,c,h} and

B = {m,a,t,h}?

The complements of B with respect

to F are elements e and c.

UNDERSTANDING

UNION OF SETS…

A = {1,2,3,4,5}B = {2,4,6,8}

A U B U C

= {1,2,3,4,5,6,8}

C = {1,3,5,7,9}

A U B

= {1,2,3,4,5,6,7,8,9}

UNION OF SETS is the set containing all the elements

found in the sets being compared. It is denoted by U.

In other words, union of sets is simply combing the elements of the sets!

REMEMBER: Do not duplicate or repeat

elements! DISTINCT

What is the union of sets P and C if P = {d,o,w,n} and

C = {l,o,a,d}?

P U C = {d,o,w,n,l,a,}

UNDERSTANDING

INTERSECTION OF SETS…

1 3 5

UA

A = {1,2,3,4,5} or A = {x|x is a number from 1 to 5}B = {2,4,6,8} or B = {x|x is a positive one-digit number}

A ∩ B 6 8

24

B

= {2,4}

INTERSECTION OF SETS is the set of all subsets that belongs

to the two sets being compared. It is denoted by ∩.

In other words, intersection of sets are the common elements for both sets.

REMEMBER: Element should be seen on both sets!

What is the intersection of sets A and I if

A = {c,l,a,r,k,s,o,n} andI = {d,a,u,g,h,t,r,y}?

A ∩ I = {a,r}

UNDERSTANDING

DISJOINT SETS…

1 3 5

7 9

UA

2 4 6 8

A = {1,3,5,7,9}B = {2,4,6,8}

= { } or A ∩ B

B

DISJOINT SETS are sets having null or empty intersection.

In other words, disjoint sets are sets without common

element.

REMEMBER: No elements are the

same!

Which of the sets are disjoint? O = {u,s,h,e,r}M = {j,u,s,t,i,n}G = {l,a,d,y,g}

O and GM and G

UNDERSTANDING

CARTESIAN PRODUCT…

A = {a,b}B = {1,2,3}

={(a,1),(a,2),(a,3),(b,1),(b,2),(b,3) }

A x B

={(1,a),(1,b),(2,a),(2,b),(3,a),(3,b) }

B x A

CARTESIAN PRODUCT is a set consisting of all the pairs of the

elements of set A to set B.

This is denoted by x.A x B is read as “A cross B”

REMEMBER: Elements in

Cartesian Product should be PAIRS!

What are the Cartesian Products of A cross B?

A = {spongebob,patrick} B = {sandy,squidward}

AxB = {(spongebob,san

dy),(sponebob,squidw

ard),(patrick,sandy),

(patrick,squidward)}

WE DID IT!Hurray!