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.
Empty, finite, infinite and equal sets. Equal sets have exactly the same elements.
Class 11 · Maths Sets FreeSubsets, the 2ⁿ subsets in a power set, and intervals as subsets of the real line.
Class 11 · Maths Sets FreeThe universal set contains everything under discussion; Venn diagrams show sets as regions.
Class 11 · Maths Sets FreeUnion, intersection, difference and complement, each a region of a Venn diagram.
Class 12 · Maths Relations and Functions FreeA relation on A is a subset of A × A. The empty and universal relations are the two extremes.
Class 12 · Maths Relations and Functions FreeThree properties of a relation, each a condition on which pairs it contains.
Class 12 · Maths Relations and Functions FreeA relation with all three properties divides its set into non-overlapping equivalence classes.
Class 12 · Maths Relations and Functions FreeOne-one: different inputs give different outputs. Onto: every codomain element is an output.
Class 12 · Maths Relations and Functions Freeg ∘ f applies f first, then g. Only bijections have inverses.
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