Class 11 Maths Chapter 1 Sets – Quick Revision Notes

Quick last-minute revision bullets covering every definition, notation, and formula in Chapter 1 — Sets. These Class 11 Mathematics Chapter 1 notes are ideal for quick revision just before exams.

Basic Definitions

• Set: a well-defined collection of distinct objects.
• Element/Member: x ∈ A (belongs), x ∉ A (does not belong).
• Roster form: elements listed within braces, e.g. {1,2,3}.
• Set-builder form: a rule describing elements, e.g. {x : x is a natural number less than 4}.

Types of Sets

• Empty/Null set (φ): no elements; n(φ)=0.
• Singleton set: exactly one element.
• Finite / Infinite sets.
• Equal sets: A=B if every element of each is in the other.
• Equivalent sets: same number of elements (need not be identical).
• Universal set (U): the overall set for a given context.

Subsets and Power Set

• Subset: A⊂B if every element of A is in B.
• Proper subset: A⊂B and A≠B.
• Empty set is a subset of every set; every set is a subset of itself.
• Power set P(A): set of all subsets of A.
• Number of subsets of an n-element set = 2ⁿ; proper subsets = 2ⁿ-1.
• If A⊂B, then P(A)⊂P(B).

Intervals as Subsets of R

• Open (a,b) = {x: a<x<b}.
• Closed [a,b] = {x: a≤x≤b}.
• Semi-open/closed [a,b) or (a,b].

Operations on Sets

• Union (A∪B): {x: x∈A or x∈B}.
• Intersection (A∩B): {x: x∈A and x∈B}.
• Disjoint sets: A∩B=φ.
• Difference (A-B): {x: x∈A and x∉B} = A∩B′.
• Complement (A′): U-A.

Key Laws and Identities

• Commutative: A∪B=B∪A; A∩B=B∩A.
• Associative: (A∪B)∪C=A∪(B∪C); (A∩B)∩C=A∩(B∩C).
• Distributive: A∪(B∩C)=(A∪B)∩(A∪C); A∩(B∪C)=(A∩B)∪(A∩C).
• Identity: A∪φ=A; A∩U=A; A∪U=U; A∩φ=φ.
• Complement: A∪A′=U; A∩A′=φ; (A′)′=A; U′=φ; φ′=U.
• De Morgan’s Laws: (A∪B)′=A′∩B′; (A∩B)′=A′∪B′.
• A=(A∩B)∪(A-B); A∪B=A∪(B-A).
• If A⊂B: A-B=φ, A∪B=B, A∩B=A.

Cardinal Number Formulas

• n(A∪B) = n(A)+n(B)-n(A∩B) (two sets); disjoint ⇒ n(A∪B)=n(A)+n(B).
• n(A-B)=n(A)-n(A∩B).
• n(A∪B∪C) = n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(A∩C)+n(A∩B∩C) (three sets).

Related NCERT Content for Class 11 Maths Chapter 1

• NCERT Solutions for Sets
• Extra Questions (HOTS) for Sets
• Class 11 Maths Formulas Handbook
• Class 11 Maths NCERT Book (Download PDF)

Written by Satish

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