Relations and Functions — Class 11 CBSE Mathematics revision notes
A 3-page visual revision sheet for Relations and Functions, 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
Relations and Functions in one look
ordered pairs, grown into a rule between two sets
- Ordered pair: order matters: (a,b)≠(b,a) unless a=b
- Cartesian product: every ordered pair (a,b) with a in A, b in B
- Relation: any subset of the Cartesian product, a chosen list of pairs
Ordered pairs and the Cartesian product
- equal exactly when both coordinates match
(a,b)=(c,d)↔ a=c, b=d - number of pairs in A×B
n(A× B)=n(A)× n(B) - Cartesian product with itself
A× A=｛(a,b) : a,bin A｝
Counting relations and functions between finite sets
- number of relations from A to B
2^n(A)n(B) - number of functions from A to B
n(B)^n(A)
Domain, co-domain, range
- domain: the set of first elements actually used, one from every pair in R
- co-domain: the WHOLE set B the relation maps into, not just the elements actually hit
- range: the set of second elements actually used, always a subset of the co-domain
- range = co-domain only when every element of B gets used at least once
A function is a fussy relation
- every relation Rsubset A× B qualifies, but a function additionally needs every element of A used exactly once
- no element of A may be left unused, and none may appear in two different pairs
- elements of B can repeat, or sit unused entirely: only A's side carries the strict rule
- written f:Ato B, and f(a)=b means the pair (a,b) belongs to f
Function notation
- a function from A to B
f:Ato B - image of a under f
f(a)=b - domain, every valid input
D_f - range, every value actually output
R_fsubset B
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Relations and Functions sheet covers
- Ordered pair
- Cartesian product
- Relation
- Ordered pairs and the Cartesian product
- equal exactly when both coordinates match
- number of pairs in A×B
- Cartesian product with itself
- Counting relations and functions between finite sets
- number of relations from A to B
- number of functions from A to B
- Domain, co-domain, range
- A function is a fussy relation
- Function notation
- a function from A to B
- image of a under f
- domain, every valid input
- range, every value actually output
- Two simple graphs
- Two more shapes
- Modulus, signum, greatest integer
- Algebra of real functions
- sum
- difference
- product
- quotient, wherever g(x)≠0
- scalar multiple
- Domains combine by overlap
- A quick worked example
- 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 Relations and Functions 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.