Sets, relations, functions and binary operations from Class 11 and 12: the language much of higher mathematics is written in, and a short, high-yield chapter group for board exams and JEE.
5 reference pages
Types of relations: reflexive, symmetric, transitive and equivalence relations, with worked examples, counting relations on a finite set, the smallest equivalence relation, and common mistakes.
Types of functions: one-one, onto, bijective and invertible functions, with worked examples, restricting a domain, counting functions between finite sets, and common mistakes.
Binary operations: closure, identity and inverse elements, commutativity and associativity, with worked examples, a count of binary operations on a finite set, and common mistakes.
How to compute gof and fog, when a composition is defined, checking an inverse by composition, and the one-one and onto properties, with worked examples.
Union, intersection, difference, complement and symmetric difference, De Morgan's laws, and inclusion-exclusion for two and three overlapping groups, with worked examples.