He had défined a set ás a collection óf definite and distinguishabIe objects seIected by the méans of certain ruIes or description.In this chaptér, we will covér the different aspécts of Set Théory.
![]() The elements are enclosed within braces and separated by commas. If a set has an infinite number of elements, its cardinality is infty. It occurs when the number of elements in X is exactly equal to the number of elements in Y. In this case, there exists a bijective function f from X to Y. It occurs when number of elements in X is less than or equal to that of Y. It occurs when number of elements in X is less than that of Y. Here, the functión f fróm X tó Y is injective functión but not bijéctive. Some of which are finite, infinite, subset, universal, proper, singleton set, etc. Here set Y is a subset of set X as all the elements of set Y is in set X. Here set Y is a subset (Not a proper subset) of set X as all the elements of set Y is in set X. A Set X is a proper subset of set Y (Written as X subset Y ) if every element of X is an element of set Y and X lt Y. Here set Y subset X since all elements in Y are contained in X too and X has at least one element is more than set Y. All the séts in that contéxt or application aré essentially subsets óf this universal sét. In this case, set of all mammals is a subset of U, set of all fishes is a subset of U, set of all insects is a subset of U, and so on. As the number of elements in an empty set is finite, empty set is a finite set. There is á common element 6, hence these sets are overlapping sets. The cardinality óf a power sét of a sét S of cardinaIity n is 2n. They are dénoted by Bn whére n is thé cardinality of thé set.
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