introduction to set theory mathematics

If two sets are given, a set can be formed by using all the elements of the two sets. Such a collection is called the union of the given sets..

The Operations on Sets are: Union of sets, Intersection of sets, Disjoint sets, Difference of two sets (Relative complement), Symmetric Difference of two sets, Complement of a set..

Two finite sets A and B are said to be equivalent sets if cardinality of both sets are equal i.e. n (A) = n (B..

The family of all subsets of any set S is called the power set of S. We denote the power set of S by P (S). If a set S is finite, say S has n elements, then the power set of S can be shown to have 2 n elemen..

Capital letters are usually used to denote or represent a set. viz., A, B, C, D, . . . . The elements of sets are usually represented by lower case letters. viz., a, b, c, x, y, . ..

Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = ..

Introduction - You are familiar with factors and products in the case of numbers. For example, 8 is the product of 4 and 2. 4 and 2 are called the products of 8 . Similarly, the algebraic expression a x b x c = abc can be written as 1.a.b.c or 1.ab.c or 1.bc.a or 1.ac.b or 1.abc. 1, a, b,..

Introduction - The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. ..