Sets, Relations and Functions Topics - IIT JEE Syllabus

1

2m1/10

📌 Key FormulaRoster form, Set-builder form, Number of elements in a set.

2

2m2/10

📌 Key FormulaA ∪ B = {x | x ∈ A or x ∈ B}, A ∩ B = {x | x ∈ A and x ∈ B}, A' = {x | x ∈ U and x ∉ A}, n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

3

2m1/10

📌 Key FormulaP(A) = set of all subsets of A, Number of elements in P(A) = 2^n(A)

4

2m1/10

📌 Key FormulaRelation as a subset of A × B, Domain and Range of a relation.

5

2m2/10

📌 Key FormulaReflexive, Symmetric, Transitive, Equivalence relations.

6

2m3/10

📌 Key FormulaEquivalence relation: Reflexive, Symmetric, Transitive. Equivalence classes.

7

2m1/10

📌 Key FormulaFunction f: A → B, Domain, Codomain, Range.

8

2m2/10

📌 Key FormulaInjective function: f(x₁) = f(x₂) ⇒ x₁ = x₂

9

2m1/10

📌 Key FormulaA function where Range is a proper subset of Codomain.

10

2m2/10

📌 Key FormulaSurjective function: Range = Codomain, ∀ y ∈ B, ∃ x ∈ A such that f(x) = y

11

2m3/10

📌 Key Formula(f ∘ g)(x) = f(g(x)), Domain of f ∘ g = {x ∈ D_g | g(x) ∈ D_f}

12

2m3/10

📌 Key Formulady/dx = - (∂f/∂x)/(∂f/∂y)