# set theory notes

An empty set contains no elements. When the subset is the set itself, it is an improper subset. Revision Notes for CBSE Class 11 Set Theory, CBSE Class 11 Mathematics Set Theory Notes. Set Operations include Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product. The National Mission for Clean Ganga (NMCG) is organising the annual ‘Ganga Utsav’ on November 2nd , 3rd & 4th, 2020 on a virtual platform. A singleton set is denoted by $\lbrace s \rbrace$. Access NCERT Solutions for Class 11 Set Theory. Important updates relating to your studies which will help you to keep yourself updated with latest happenings in school level education. The set difference of sets A and B (denoted by $A – B$) is the set of elements which are only in A but not in B. The union of two sets is a set containing all the numbers in those sets, but any duplicates are only written once. Let $S = \lbrace 1, 2, 3\rbrace$, $n = |S| = 3$, 2. When the subset is missing some elements that are in the set it is being compared to, it is a proper subset. We intend to give educational materials to the students for the betterment of grades. Click here to download NCERT Solutions for questions of Class 11 Set Theory NCERT Book. The total number of subsets of a finite set containing n elements is 2 n. Intervals as Subsets of R Let a and b be two given real numbers such that a < b, then. Hence, we can write $Y \subseteq X$. Download Revision Notes for CBSE Class 11 Set Theory. The A represents all the elements in the smaller oval; the B represents all the elements in the larger oval; and the C represents all the elements that are in both ovals at the same time. {1,2,3} is the set consisting of only the elements 1,2, and 3. Keep yourself updated with all latest news and also read articles from teachers which will help you to improve your studies, increase motivation level and promote faster learning. Bell numbers give the count of the number of ways to partition a set. Hence, $A \cap B = \lbrace x \:|\: x \in A\ AND\ x \in B \rbrace$. NB (Note Bene) - It is almost never necessary in a mathematical proof to remember that a function is literally a set of ordered pairs. All revision notes and short key-notes are prepared from the latest edition of Class 11 books and upcoming exams. Note that the empty set is a subset of every set. When the subset is the set itself, it is an improper subset. A set which contains infinite number of elements is called an infinite set. The number is also referred as the cardinal number. Sets and elements Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. The set is described as $A = \lbrace x : p(x) \rbrace$, Example 1 − The set $\lbrace a,e,i,o,u \rbrace$ is written as −, $A = \lbrace x : \text{x is a vowel in English alphabet} \rbrace$, Example 2 − The set $\lbrace 1,3,5,7,9 \rbrace$ is written as −, $B = \lbrace x : 1 \le x \lt 10 \ and\ (x \% 2) \ne 0 \rbrace$. The function f: A!Bis an injection i(8a;a02 A) if a6= a0then f(a) 6= f(a0) Denition 1.9 (Surjection). © 2020 Houghton Mifflin Harcourt. Figure 2. Here set Y is a subset (Not a proper subset) of set X as all the elements of set Y is in set X. Equivalent sets are sets that have the same number of members — {1, 2, 3} | { a, b, c}. The revision notes always keep a track of all the information you have learned. It occurs when number of elements in X is less than that of Y. $|X| \lt |Y|$ denotes that set X’s cardinality is less than set Y’s cardinality. In this chapter, we will cover the different aspects of Set Theory. $\lbrace 1 \rbrace , \lbrace 2 \rbrace , \lbrace 3 \rbrace$, If $S = \lbrace1, 1.2, 1.7, 2\rbrace , 1 \in S$ but $1.5 \notin S$, $\lbrace 1 \rbrace , \lbrace 2, 3 \rbrace$, $\lbrace 1, 2 \rbrace , \lbrace 3 \rbrace$, $\lbrace 1, 3 \rbrace , \lbrace 2 \rbrace$, $\lbrace 1 \rbrace , \lbrace 2 \rbrace , \lbrace 3 \rbrace$, A set of all the planets in the solar system, A set of all the lowercase letters of the alphabet. When the subset is missing some elements that are in the set it is being compared to, it is a proper subset. All the sets in that context or application are essentially subsets of this universal set. $| P (\lbrace \emptyset \rbrace) | = 2^0 = 1$, Partition of a set, say S, is a collection of n disjoint subsets, say $P_1, P_2, \dots P_n$ that satisfies the following three conditions −, $\lbrack P_i \ne \lbrace \emptyset \rbrace\ for\ all\ 0 \lt i \le n \rbrack$. Therefore, disjoint sets have the following properties −. In order to reach out to maximum students across the country, the Board will host the Aryabhata Ganit Challenge on DIKSHA platform... With a larger goal to promote 21st century skills such as critical thinking and problem solving, the Central Board of Secondary Education has shared a Mathematical Literacy: Practice Book for Students. The cardinality of empty set or null set is zero. Practice test sheets for Class 11 for Set Theory made for important topics in NCERT book 2020 2021 available for free... Free CBSE Class 11 Set Theory Online Mock Test with important multiple choice questions as per CBSE syllabus. This Work Book is designed to allow learners of classes 7th to 10th... You can download notes for Class 11 Set Theory for latest 2020 session from StudiesToday.com, Yes - You can click on the links above and download chapterwise Notes PDFs for Class 11 Set Theory, Yes - The Notes issued for Class 11 have been made available here for latest 2020 session, You can easily access the links above and download the Class 11 Notes for Set Theory for each chapter, Yes - Studiestoday team has also provided free Class 11 solutions for all questions, There is no charge for the Notes for Class 11 you can download everything free, Yes - Apart from Class 11 Set Theory you can download Notes and related study material for all other subjects in Class 11 for year 2020. Power set is denoted as $P(S)$. $|A| = |B| = 3$. Role of Word Limit in Written CBSE Examination, What to do Post Receipt of Question Paper in the Board Examination, Mathematical Literacy Free Practice Book for Students, Principle of Mathematical Induction (PMI). If you were to let the set with {1,2,3} be set A, and the set with {3,4,5} be set B, then you could use Venn diagrams to illustrate the situation (see Figure 2). The Utsav will involve storytelling, folklores, & dialogues with eminent personalities, quizzes, display of traditional... CBSE has launched a Quiz on Mahatma Gandhi. We start with the basic set theory. If the cardinalities of two sets are same, they are called equivalent sets. Set Theory. It occurs when the number of elements in X is exactly equal to the number of elements in Y. We believe in building a education system that can benefit an individual for the development of nation as a whole. (Caution: sometimes ⊂ is used the way we are using ⊆.) Save my name, email, and website in this browser for the next time I comment. If an element x is a member of any set S, it is denoted by $x \in S$ and if an element y is not a member of set S, it is denoted by $y \notin S$. Removing #book# Verbally, “3 is an element of the set {1,2,3}.” To show this symbolically, use the symbol ∈, which is read as “is an element of” or “is a member of.” Therefore, you could have written: A subset is a set contained within another set, or it can be the entire set itself. The empty set, or null set, is the set with no elements or members.

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