Category: 01. Sets Theory

Let A, B be any two finite sets. Then n (A ∪ B) = n (A) + n (B) – n (A ∩ B) Here “include” n (A) and n (B) and we “exclude” n (A ∩ B) Example 1: Suppose A, B, C are finite sets. Then A ∪ B ∪ C is finite…

A multiset is an unordered collection of elements, in which the multiplicity of an element may be one or more than one or zero. The multiplicity of an element is the number of times the element repeated in the multiset. In other words, we can say that an element can appear any number of times…

Sets under the operations of union, intersection, and complement satisfy various laws (identities) which are listed in Table 1. Table: Law of Algebra of Sets Idempotent Laws (a) A ∪ A = A (b) A ∩ A = A Associative Laws (a) (A ∪ B) ∪ C = A ∪ (B ∪ C) (b) (A…

The basic set operations are: 1. Union of Sets: Union of Sets A and B is defined to be the set of all those elements which belong to A or B or both and is denoted by A∪B. Example: Let A = {1, 2, 3},       B= {3, 4, 5, 6}A∪B = {1, 2, 3,…

Sets can be classified into many categories. Some of which are finite, infinite, subset, universal, proper, power, singleton set, etc. 1. Finite Sets: A set is said to be finite if it contains exactly n distinct element where n is a non-negative integer. Here, n is said to be “cardinality of sets.” The cardinality of sets…

A set is defined as a collection of distinct objects of the same type or class of objects. The purposes of a set are called elements or members of the set. An object can be numbers, alphabets, names, etc. Examples of sets are: We broadly denote a set by the capital letter A, B, C,…