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    Assignment - A Q1. A) What Is A Set? Explain Various Methods To Represent A Setin Set Theory - Ans 1a)

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    Sadiksha Sharma
    A set is a collection of distinct objects considered as a whole. Sets can be represented using the roster method, which lists the elements, or the rule method, which describes the properties of the elements. The document provides examples of each representation method. It also defines singleton sets as sets with exactly one element, finite sets as sets with a finite number of elements, cardinality as the number of elements in a set, and subsets as sets where all elements of one set are also elements of another set.

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    Assignment - A Q1. A) What Is A Set? Explain Various Methods To Represent A Setin Set Theory - Ans 1a)

    Uploaded by

    Sadiksha Sharma
    16 views6 pages
    A set is a collection of distinct objects considered as a whole. Sets can be represented using the roster method, which lists the elements, or the rule method, which describes the properties of the elements. The document provides examples of each representation method. It also defines singleton sets as sets with exactly one element, finite sets as sets with a finite number of elements, cardinality as the number of elements in a set, and subsets as sets where all elements of one set are also elements of another set.

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    A set is a collection of distinct objects considered as a whole. Sets can be represented using the roster method, which lists the elements, or the rule method, which describes the properties of the elements. The document provides examples of each representation method. It also defines singleton sets as sets with exactly one element, finite sets as sets with a finite number of elements, cardinality as the number of elements in a set, and subsets as sets where all elements of one set are also elements of another set.

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    Attribution Non-Commercial (BY-NC)
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    Download as docx, pdf, or txt
    16 views6 pages

    Assignment - A Q1. A) What Is A Set? Explain Various Methods To Represent A Setin Set Theory - Ans 1a)

    Uploaded by

    Sadiksha Sharma
    A set is a collection of distinct objects considered as a whole. Sets can be represented using the roster method, which lists the elements, or the rule method, which describes the properties of the elements. The document provides examples of each representation method. It also defines singleton sets as sets with exactly one element, finite sets as sets with a finite number of elements, cardinality as the number of elements in a set, and subsets as sets where all elements of one set are also elements of another set.

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    Assignment - A Q1. a) What is a Set? Explain various methods to represent a setin set theory.

    Ans 1a): A set is a group or collection of objects or numbers, considered as an entityunto itself. Sets are usually symbolized by uppercase, italicized, boldface letters such as A, B, S, or Z. Each object or number in a set is called a member or element of the set.Examples include the set of all computers in the world, the set of all apples on a tree,and the set of all irrational numbers between 0 and 1.When the elements of a set can be listed or enumerated, it is customary to enclose thelist in curly brackets. Thus, for example, we might speak of the set (call it K) of allnatural numbers between, and including, 5 and 10 as:K = {5, 6, 7, 8, 9, 10}

    Methods to represent a set: There are two methods to represent a set. One is Rule method, another one is Roster method.Rule is a method of naming a set by describing its elements.For example, { x: x > 3, x is a whole number} describes the set with elements 4, 5, 6,.T h e r e f o r e , { x : x > 3 , x i s a w h o l e n u m b e r } i s t h e s a m e a s { 4 , 5 , 6 , } . { x : x > 3 } describes all numbers greater than 3. This set of numbers cannot be represented as alist and is represented using a number line graph.Roster is a method of naming a set by listing its members. For example, {1,2,3} is theset consisting of only the elements 1,2, and 3. There are many ways to represent thisset using a rule.Two correct methods are as follows:{x: x < 4, x is a natural number} {x: 0 < x < 4, x is a whole

    number} An incorrect method would be {x:0 < x < 4} because this rule includes ALL numbersbetween 0 and 4, not just the numbers 1, 2, and 3. Q1 b): Define the following with the help of suitable examples. () i Singleton Set () ii Finite Set () iii Cardinality of a Set () iv Subset of a SetAns 1b): Singleton Set A set having exactly one element is called Singleton set. A singleton set is denoted byand is the simplest example of a nonempty set. Any set other than the empty set istherefore a nonempty set. For example {a} Finite Sets:

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