Quant · Modern Maths

Set Theory and Venn Diagrams

3 sub-topics · 22 lessons · 62 questions · 14 PYQs

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Two-Set Venn Problems7 lessons · 24 questions · 6 PYQs

Three-Set Venn Problems8 lessons · 20 questions · 6 PYQs

Set Algebra and Power Sets7 lessons · 18 questions · 2 PYQs

Formula sheet

Sum of the sizes of two sets
$n(A)+n(B)=n(A\cup B)+n(A\cap B)$
Union of two sets
$n(A\cup B)=n(A)+n(B)-n(A\cap B)$
Least and greatest union
$\max(n(A),n(B))\le n(A\cup B)\le\min(n(U),\ n(A)+n(B))$
Least and greatest overlap
$\max(0,\ n(A)+n(B)-n(U))\le n(A\cap B)\le\min(n(A),n(B))$
Inclusion-exclusion for three sets
$n(A\cup B\cup C)=\sum n(A)-\sum n(A\cap B)+n(A\cap B\cap C)$
Power sets of the empty set
$n(\emptyset)=0\to n(P(\emptyset))=1\to 2\to 4\to 16\to 65536$
Difference and De Morgan's laws
$A-B=A\cap B',\quad (A\cup B)'=A'\cap B',\quad (A\cap B)'=A'\cup B'$
Distributive laws for sets
$A\cap(B\cup C)=(A\cap B)\cup(A\cap C),\quad A\cup(B\cap C)=(A\cup B)\cap(A\cup C)$