Chapter 1 — Sets

Chapter 1 of the Class 11 Maths NCERT textbook, "Sets", introduces the well-defined collection of objects that underpins all of modern mathematics. Georg Cantor developed set theory in the 1870s while studying trigonometric series.

• Sets as the foundation of mathematics — The chapter frames a set as a well-defined collection whose membership is always decidable, then shows why this single idea sits under geometry, sequences, probability and every other branch you meet later in the course.
• Describing and classifying sets — You learn to write sets two ways — roster form listing elements and set-builder form stating a property — and to sort them as empty, finite or infinite, giving a shared vocabulary for talking precisely about collections.
• Operations and the algebra of sets — Union, intersection, difference and complement combine sets into new ones, and these operations obey structural laws like commutativity, associativity and distributivity — turning set manipulation into a genuine algebra.

1. 01A set is a well-defined collection of objects; membership is always decidable
2. 02Two representation methods: roster form {1,2,3} and set-builder form {x: condition}
3. 03Empty set (φ) contains no elements; finite sets have definite cardinality; infinite sets have unlimited elements
4. 04A subset (A ⊂ B) means every element of A is also in B; proper subsets exclude equality
5. 05Set operations include union (∪), intersection (∩), difference (-), and complement ('); follow commutativity, associativity, and distributivity laws
6. 06De Morgan's laws: (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'