2. Universal SetThe Universal Set is theset that
containseverything. Well,not exactlyeverything. Everything that we
areinterested in now.Sadly, the symbol is theletter "U" ... which
is easyto confuse with the forUnion. You just have to becareful,
OK?In our case the UniversalSet is our Ten BestFriends.U = {alex,
blair, casey,drew, erin, francis, glen,hunter, ira, jade}We can
show theUniversal Set in a Venn 3. Now you can see ALLyour ten best
friends,neatly sorted intowhat sport they play(or not!).And then we
can dointeresting things liketake the whole setand subtract theones
who playSoccer: 4. We write it this way:U S = {blair, erin,
francis, glen, ira, jade}Which says "The Universal Set minus the
SoccerSet is the Set {blair, erin, francis, glen, ira, jade}"In
other words "everyone who does not playSoccer". 5. ComplementAnd
there is a specialway of saying"everything thatis not", and it
iscalled "complement".We show it by writinga little "C" like
this:SWhich means"everything that isNOT in S", like this: 6. S =
{blair,erin, francis,glen, ira, jade}(just like the U C examplefrom
above) 7. Summary is Union: is in either set isIntersection: must
be in bothsets is Difference: in one set butnot the otherAc is
theComplement of A: everything thatis not in AEmpty Set: the set
withno elements. Shown by{}Universal Set: all things we
areinterested in 8. Ten Best FriendsYou could have a set made up of
your tenbest friends:{alex, blair, casey, drew, erin, francis,
glen,hunter, ira, jade}Each friend is an "element" (or "member")of
the set (it is normal to use lowercaseletters for them.)Now let's
say that alex, casey, drew andhunter play Soccer:Soccer = {alex,
casey, drew, hunter}(The Set "Soccer" is made up of theelements
alex, casey, drew and hunter). 9. And casey, drew andjade play
Tennis:Tennis = {casey, drew,jade}You could put theirnames in
twoseparate circles: 10. UnionYou can now list yourfriends that
play SoccerOR Tennis.This is called a "Union"of sets and has
thespecial symbol :Soccer Tennis = {alex,casey, drew,
hunter,jade}Not everyone is in thatset ... only your friendsthat
play Soccer orTennis (or both).We can also put it in a"Venn
Diagram": 11. A Venn Diagram is clever becauseit shows lots of
information:Do you see that alex, casey, drewand hunter are in the
"Soccer" set?And that casey, drew and jade arein the "Tennis"
set?And here is the clever thing: caseyand drew are in BOTH sets!
12. Intersection"Intersection" is whenyou have to be in BOTHsets.In
our case thatmeans they play bothSoccer AND Tennis ...which is
casey anddrew.The special symbol forIntersection is an upsidedown
"U" like this: And this is how we writeit down:Soccer Tennis
={casey, drew}In a Venn Diagram: 13. Which Way Does That"U"
Go?Think of them as"cups": would holdmore water than ,right?So
Union is the onewith more elementsthan Intersection 14.
DifferenceYou can also "subtract"one set from another.For example,
takingSoccer and subtractingTennis means peoplethat play Soccer
butNOT Tennis... which isalex and hunter.And this is how we writeit
down:Soccer Tennis = {alex,hunter}In a Venn Diagram: 15. Summary:
is Union: is in either set is Intersection: must be in both sets is
Difference: in one set but not the other 16. Three SetsYou can also
use VennDiagrams for 3 sets.Let us say the third setis
"Volleyball", whichdrew, glen and jadeplay:Volleyball = {drew,
glen,jade}But let's be more"mathematical" and usea Capital Letter
for eachset:S means the set ofSoccer playersT means the set
ofTennis playersV means the set ofVolleyball players 17. You can
see (forexample) that:drew plays Soccer,Tennis and Volleyballjade
plays Tennis andVolleyballalex and hunter playSoccer, but don't
playTennis or Volleyballno-oneplays only Tennis 18. We can nowhave
some funwith Unions andIntersections ...This is just theset SS =
{alex,casey, drew,hunter} 19. This is theUnion of Sets Tand VT V =
{casey,drew, jade,glen} 20. This isthe Intersection of Sets S andVS
V = {drew} 21. And how about this ...take the previousset S Vthen
subtract T:This is the Intersectionof Sets S andV minus Set T(S V)
T = {}That is OK, it is just the"Empty Set". It is still aset, so
we use thecurly brackets withnothing inside: {}The Empty Set has
noelements: {}
