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
Reflexive, symmetric, transitive, and equivalence relations defined and checked against worked examples.
One-one, onto, bijective, and invertible functions explained, with worked examples on checking each property and finding an inverse.
What a binary operation is, and how to check whether one has an identity element, is commutative, or is associative, with worked examples.
How to compute the composition of two functions in either order, with a worked example showing gof and fog can come out different.
Union, intersection, and the inclusion-exclusion principle for counting overlapping groups, with a worked example.