MATH MIND MAPS
Relations & Functions • Inverse Trig • Matrices
Class 12 | Chapter Summaries
3 Chapters Key Formulas All Definitions
, RELATIONS 01
Let A and B be non-empty sets. R ⊆ A×B is called a Relation. If (a,b) ∈ R, we write aRb.
Empty Relation Universal Relation
R = ϕ ⊆ A×A (no element related to any) R = A×A (every element related to every)
Identity Relation Reflexive Relation
I_A = {(a,a) : a ∈ A} (each related to itself) (a,a) ∈ R for every a ∈ A
Symmetric Relation Transitive Relation
(a,b) ∈ R ⟹ (b,a) ∈ R for all a,b ∈ A (a,b) ∈ R and (b,c) ∈ R ⟹ (a,c) ∈ R
Equivalence Relation Equivalence Class [a]
Reflexive + Symmetric + Transitive {b ∈ A : (a,b) ∈ R} — set of all elements related to a
Relations & Functions • Inverse Trig • Matrices
Class 12 | Chapter Summaries
3 Chapters Key Formulas All Definitions
, RELATIONS 01
Let A and B be non-empty sets. R ⊆ A×B is called a Relation. If (a,b) ∈ R, we write aRb.
Empty Relation Universal Relation
R = ϕ ⊆ A×A (no element related to any) R = A×A (every element related to every)
Identity Relation Reflexive Relation
I_A = {(a,a) : a ∈ A} (each related to itself) (a,a) ∈ R for every a ∈ A
Symmetric Relation Transitive Relation
(a,b) ∈ R ⟹ (b,a) ∈ R for all a,b ∈ A (a,b) ∈ R and (b,c) ∈ R ⟹ (a,c) ∈ R
Equivalence Relation Equivalence Class [a]
Reflexive + Symmetric + Transitive {b ∈ A : (a,b) ∈ R} — set of all elements related to a
