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Sessions

Short interactive lessons that ask a question before they explain. One session takes about ten minutes and ends with questions to check what you have understood.

All Class 9 Class 10 Class 11 Class 12 Science Physics Chemistry Maths
SESSION 6 6 Solutions Class 12 · Chemistry Solutions Free

Abnormal molar mass and the van't Hoff factor

Dissociation and association change the number of particles. The van’t Hoff factor i corrects for it.

SESSION 1 1 Relations and Functions Class 12 · Maths Relations and Functions Free

What a relation is

A relation on A is a subset of A × A. The empty and universal relations are the two extremes.

SESSION 2 2 Relations and Functions Class 12 · Maths Relations and Functions Free

Reflexive, symmetric, transitive

Three properties of a relation, each a condition on which pairs it contains.

SESSION 3 3 Relations and Functions Class 12 · Maths Relations and Functions Free

Equivalence relations and classes

A relation with all three properties divides its set into non-overlapping equivalence classes.

SESSION 4 4 Relations and Functions Class 12 · Maths Relations and Functions Free

One-one, onto, and bijective functions

One-one: different inputs give different outputs. Onto: every codomain element is an output.

SESSION 5 5 Relations and Functions Class 12 · Maths Relations and Functions Free

Composition and inverse

g ∘ f applies f first, then g. Only bijections have inverses.

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