Download - Operations on sets
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OPERATIONS ON SETSby: Teacher MYRA CONCEPCION
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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}
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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!
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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!
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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}
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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!
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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.
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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}
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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.
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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}
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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
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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,}
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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}
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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!
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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}
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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
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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!
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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
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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
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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!
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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)}
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WE DID IT!Hurray!