1. SETS
1. A setis a collectionof things,thathave acommon qualitye.g.The setof evennumbers
2. A setcan be emptyorknownas the null setrepresentedas ∅ or{ }
3. The membersoff a setare calleditselements
4. A setcan be namede.g.LetA be the set of evennumbers.Therefore A={2,4,6,8,...}
5. A setcan be describedinwordse.g.the setof whole numbersup toten OR listede.g.
{0,1,2,3,4,5,6,7,8,9, 10} or eveninnotationwhere A = {W ≤ 10}
6. Setscan be finite meaningtheyhave definiteborderse.g.The Natural numbersupto5 –
{1,2,3,4,5} or infinite meaningnever-endinge.g.the setof Integers –{...-3,-2,-1,0,1,2,3,...}
7. Setsare representedonaVenn diagraminventedbyJosephVenn.Itisalwaysdrawnasa large
rectangle toshowthe Universal set
8. Setcan be subsetsof othersetsmeaningasetcan containanotherentirely.
9. The Universal setisalwaysthe setwhichcontainseverything.
10. Whendoingsetspay attentiontothe wordONLY. It will indicatewhere avalue mustbe placed
ina Venn diagram. Forinstance,there isa difference between,the Boyslove toplayFootball
and the boyswholove to playFootball ONLY.
11. You will neverbe askedtomanipulate more than3setsin anyquestion
12. The numberof subsetsinanysetis givenbythe formula 2 𝑛 where nisthe numberof members
or elementinthe set
13. If sets donot intersectthentheyare calleddisjoint
14. Setscan be equal once theyhave exactlythe same elements
15. SET SYMBOLS:-
 ⊂ – MEANS ISA SUBSET OF.Note that thissigncan be turnedaroundlike this ⊃ andmeans
containsor ‘isa supersetof’ ∴ we can say A ⊂ B meaningA is a subsetof B OR B ⊃ A meaningB
containsA or B isa Supersetof A
 E/𝜀 /∈ MEANS IS A MEMBER OF/ ISAN ELEMENT OF
 ∉ MEANS IS NOTAN ELEMENT OF
 U – MEANS THE UNION OF SETS (oreverythinginthe twoor three sets)
 ∩ MEANSTHE INTERSECTION OFSETS (oronlythe commonmembers/elementsof the sets)
 𝑛( 𝐴)MEANS THE NUMBER OF ELEMENTS (not subsets) inthe setA (e.g.N(AUB) meansthe
numberof elementsin A unionB)
 A’MEANS THE COMPLEMENT OFSET A (oreverythingOUTSIDEof setA)