Sets and Relations — Class 11 Maharashtra HSC Mathematics revision notes
A 6-page visual revision sheet for Sets and Relations, written for Class 11 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Sets and Relations in one look
a well-defined collection, the operations that combine two of them, and the ordered pairs that link them
What Makes a Set
- a set is a collection of WELL-DEFINED objects, called its elements or members
- well-defined means anyone can decide, without opinion, whether an object belongs
- 'days in a week' is well-defined, 'happy people in a town' is not
- xin A reads x belongs to A; xnotin A reads x does not belong to A
- three ways to describe a set: roster, set-builder, and a Venn diagram
- roster lists every element in braces; order and repeats don't matter
- set-builder states the defining property instead of listing members
- n(A), the cardinality of A, is the count of distinct elements in a finite set A
Types of Sets
- Empty set: no elements at all, written φ or ｛｝; n(φ)=0
- Singleton: exactly one element, n(A)=1
- Finite: a finite number of elements, including the empty set itself
- Infinite: not finite: the natural numbers, or all points on a circle
- Equal sets: A=B exactly when Asubseteq B and Bsubseteq A: same elements, order and repeats irrelevant
- Equivalent sets: n(A)=n(B): same SIZE, not necessarily the same elements
- Subset: Asubseteq B: every element of A lies in B
- Proper subset: Asubset B: Asubseteq B, plus at least one element of B outside A
- Power set P(A): the set of all subsets of A, itself a set of sets. n(A)=m gives n(P(A))=2^m
Universal Set
- every set in a discussion sits inside one fixed U: the universal set
- φsubseteq every set, and every set subseteq itself
Page 1 of 6. The full sheet, all 6 pages, opens free in the app.
What this Sets and Relations sheet covers
- What Makes a Set
- Types of Sets
- Empty set
- Singleton
- Finite
- Infinite
- Equal sets
- Equivalent sets
- Subset
- Proper subset
- Power set P(A)
- Universal Set
- Operations on Sets
- De Morgan's Laws
- Counting Formulas
- two sets
- disjoint sets
- three sets
- symmetric difference
- power set
- The union formula, special cases
- Intervals on the Real Line
- Ordered Pairs and the Cartesian Product
- Relation, Domain, Co-domain, Range
- Types of Relations on a Set
- Reflexive, symmetric, transitive: not automatic together
- Congruence Modulo m
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Sets and Relations the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.