Ch 1 introduces the language of sets — the foundation of modern mathematics. Students learn to represent sets, classify them, perform operations, and use Venn diagrams to visualise relationships.
Sets are described in roster form {1,2,3} or set-builder form {x: x is even}. Types: empty/null set (∅), finite, infinite, equal, equivalent, subsets, power set. The power set of a set with n elements has 2ⁿ elements.
Union (A∪B): all elements in A or B. Intersection (A∩B): elements common to both. Difference (A−B): elements in A but not B. Complement (A'): elements in universal set U but not in A.
Commutative: A∪B = B∪A. Associative: (A∪B)∪C = A∪(B∪C). Distributive: A∩(B∪C) = (A∩B)∪(A∩C). De Morgan's: (A∪B)' = A'∩B' and (A∩B)' = A'∪B'.
Download: https://ncert.nic.in/textbook/pdf/kemh101.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
The power set P(A) of set A is the set of all subsets of A, including ∅ and A itself. If A has n elements, P(A) has 2ⁿ elements. For example, P({1,2}) = {∅, {1}, {2}, {1,2}} — 4 elements.
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