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Multisets, Multiplicity, Equality, MultiSubset, Union, Intersection, Difference, Sum, and related Topics.
Sets, Set Notations, Subset / Proper Subset, Universal Set, Set Operations: Complement, Set Operations: Union, Set Operations: Intersection, Disjoint Sets, Properties: Set Operations, and other topics.
Set Operations: Difference, Properties: Difference, Set Operations: Symmetric Diffrence, Properties: Symmetric Difference, Cardinality, Power Set, Laws: Set Operations, Proofs, and other topics.
Introduction, Partitions of a Set, Principle of Inclusion Exclusion, Proof, Corollary, Example, and other topics.
Multisets, Multiplicity, Equality, MultiSubset, Union, Intersection, Difference, Sum, and other topics.
Inverse of an Element, Group, Abelian Group, Order of a Group, Order of An element, Cyclic Group, Product Group, Properties of a Group, Sub-Group, Cosets, Properties of a Coset, and other topics.
Introduction, n-ary operation, Algeraic System, Binary Operations, Semi-Group, Residue Class Modulo n, Identity, Monoid, and other topics.
Properties of Cosets (contd...), Lagrange's Theorem, Normal Subgroup, Qotient Group, Group Homomorphism, Group Automorphism, Group Isomorphism, and other topics.
Rings, Commutative Ring, Ring with no proper Divisors of 0, Ring with a unity, Unit of a Ring, Integral Domain, Field, Properties of Rings, Example, and other topics.