Sets — Class 11 CBSE Mathematics revision notes
A 3-page visual revision sheet for Sets, written for Class 11 CBSE 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 in one look
a well-defined collection, and every operation you can build from it
- Set: a well-defined collection of distinct objects
- Roster form: every element listed, comma-separated. Order and repeats don't matter
- Set-builder form: a rule the elements must satisfy, instead of a list
Five kinds of sets
- Empty set: ∅: no elements at all, n(A)=0
- Finite set: counting the elements ends somewhere, n(A) is a whole number
- Infinite set: counting never ends. N, Z, R are all infinite
- Singleton set: exactly one element, n(A)=1
- Equal sets: A=B when every element of A is in B, and every element of B is in A
Subsets and the power set
- Asubset B when every element of A is also in B
- every set is a subset of itself, and ∅ is a subset of every set, even of itself
- proper subset: Asubset B but A≠ B, at least one element of B is left out
- power set P(A) is the set of all subsets of A, ∅ and A included
- n(A)=n ⇒ n(P(A))=2^n
Universal set and Venn diagrams
- the universal set U holds every element under discussion. Every other set here sits inside it
- a Venn diagram draws U as a rectangle, each set as a circle inside it, elements as dots
- where two circles overlap is exactly Acap B. Draw the picture before you compute
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Sets sheet covers
- Set
- Roster form
- Set-builder form
- Five kinds of sets
- Empty set
- Finite set
- Infinite set
- Singleton set
- Equal sets
- Subsets and the power set
- Universal set and Venn diagrams
- The four operations
- union: in A or B, or both
- intersection: only what's common to both
- difference: in A but not in B
- complement: everything in U except A
- Union vs intersection: bigger picture or common ground
- Union, A∪B
- Intersection, A∩B
- Complement laws
- De Morgan's laws
- complement of a union
- complement of an intersection
- Cardinal number of a union
- two sets
- disjoint sets, Acap B=∅
- Distributive laws
- intersection distributes over union
- union distributes over intersection
- Symmetric difference, one more operation
- in exactly one of the two, not both
- its cardinal number
- Intervals as sets
- closed, both ends included
- open, both ends excluded
- semi-open, left end excluded
- Symbols
- 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 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.