IGCSE›Cambridge IGCSE Maths›Mind mapsSet Notation & Venn DiagramsCambridge IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsWhat is a set?A well-defined collection of elementsNamed with capitals, curly brackets: A={2,4,6,8}A = \{2, 4, 6, 8\}A={2,4,6,8}Rule form: A={x:x is a natural number}A = \{x : x \text{ is a natural number}\}A={x:x is a natural number}C={x:a≤x≤b}C = \{x : a \leq x \leq b\}C={x:a≤x≤b} includes both endsNotationn(A)n(A)n(A) = number of elements in AA′A'A′ = complement, everything not in AE\mathcal{E}E = universal setA∪BA \cup BA∪B = union, in A or BA∩BA \cap BA∩B = intersection, in bothA⊆BA \subseteq BA⊆B = subset; x∈Ax \in Ax∈A = element ofSets & Vennset notation∪\cup∪∩\cap∩A′A'A′∅\emptyset∅Venn diagramsOverlapping circles inside a rectangle for E\mathcal{E}EOverlap holds the intersectionOutside circles but inside rectangle = neitherCore: two circles; Extended: up to threeSolving problemsn(A∪B)=n(A)+n(B)−n(A∩B)n(A \cup B) = n(A) + n(B) - n(A \cap B)n(A∪B)=n(A)+n(B)−n(A∩B)30 students, 18 French, 15 Spanish, 8 bothOnly French = 18−8=1018 - 8 = 1018−8=10n(F∪S)=10+8+7=25n(F \cup S) = 10 + 8 + 7 = 25n(F∪S)=10+8+7=25Neither = 30−25=530 - 25 = 530−25=5Exam tipsFill the innermost overlap first, then work outwardNever add n(F)n(F)n(F) and n(S)n(S)n(S) alone: double-counts the overlap