# set theory notes

$|A| = |B| = 3$. In naive set theory, a set is a collection of objects (called members or elements) that is regarded as being a single object. If a set has an infinite number of elements, its cardinality is $\infty$. Here, there exists an injective function ‘f’ from X to Y. $\lbrace 1 \rbrace , \lbrace 2, 3 \rbrace$, 3. When the subset is missing some elements that are in the set it is being compared to, it is a proper subset. The revision notes always keep a track of all the information you have learned. Example − $S = \lbrace x \:| \:x \in N,\ 7 \lt x \lt 9 \rbrace$ = $\lbrace 8 \rbrace$. Introduction to naive set theory Fundamental set concepts. When there is the possibility of using an imprope… As such, it is expected to provide a ﬁrm foundation for the rest of mathematics. For example, { a,b,c,d,e} is a set of five elements, thus it is a finite set. Denition 1.8 (Injection). Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. Such a relation between sets is denoted by A ⊆ B. Example − Let, $A = \lbrace 1, 2, 6 \rbrace$ and $B = \lbrace 6, 12, 42 \rbrace$. Venn diagram, invented in 1880 by John Venn, is a schematic diagram that shows all possible logical relations between different mathematical sets. CliffsNotes study guides are written by real teachers and professors, so no matter what you're studying, CliffsNotes can ease your homework headaches and help you score high on exams. Equal sets are those that have the exact same members — {1, 2, 3} = {3, 2, 1}. It is natural for us to classify items into groups, or sets, and consider how those sets overlap with each other. an open interval denoted by (a, b) is the set of real numbers {x : a < x < b}. Example − If $A = \lbrace 1, 2, 6 \rbrace$ and $B = \lbrace 16, 17, 22 \rbrace$, they are equivalent as cardinality of A is equal to the cardinality of B. i.e. Two correct methods are as follows: An incorrect method would be { x:0 < x < 4} because this rule includes ALL numbers between 0 and 4, not just the numbers 1, 2, and 3. We intend to give educational materials to the students for the betterment of grades. 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 $Y$. $\lbrace 1, 2 \rbrace , \lbrace 3 \rbrace$, 4. Set Theory. The empty set, or null set, is represented by ⊘, or { }. 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. The cardinality of a power set of a set S of cardinality n is $2^n$. The intend of this article is to guide the students about the course of action they should follow once they receive the CBSE question papers in the school as well as board examination centre. Enter pincode to get tutors in your city. Access NCERT Solutions for Class 11 Set Theory. The cardinality of empty set or null set is zero. Here set Y is a subset (Not a proper subset) of set X as all the elements of set Y is in set X. $\lbrace 1 \rbrace , \lbrace 2 \rbrace , \lbrace 3 \rbrace$, 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. Example 2 − Let, $X = \lbrace 1, 2, 3 \rbrace$ and $Y = \lbrace 1, 2, 3 \rbrace$. But even more, Set Theory is the milieu in which mathematics takes place today. The intersection of sets A and B (denoted by $A \cap B$) is the set of elements which are in both A and B. For example, number 8, 10, 15, 24 are the 4 distinct numbers, but when we put them together, they form a set of 4 elements, such that, {8, 10, 15, 24}. Rule is a method of naming a set by describing its elements. Prepared by standard 11 teachers will help you to understand difficult and complex Set Theory topics and to revise quickly before tests and exams. The set {1,2} is a subset of the set {1,2,3}, and the set {1,2,3} is a subset of the set {1,2,3}. Example − If $A = \lbrace 11, 12, 13 \rbrace$ and $B = \lbrace 13, 14, 15 \rbrace$, then $A \cap B = \lbrace 13 \rbrace$. Notebahadur.com is a site created solely for educational purposes. Therefore, {1,2} ⊂ {1,2,3} and {1,2,3} ⊆ {1,2,3}. Hence, $A \cap B = \lbrace x \:|\: x \in A\ AND\ x \in B \rbrace$. The set {1,2} is a subset of the set {1,2,3}, and the set {1,2,3} is a subset of the set {1,2,3}. The study material has been made by experienced teachers of leading schools and institutes in India is available for free download in pdf format. The term “proper subset” can be defined as “subset of but not equal to”. Where can I download latest 2020 Class 11 Set Theory notes ? The elements are enclosed within braces and separated by commas. Note: Every set is o subset of itself. Figure 2. Regularly revise these exam notes as these will help you to cover all important topics in NCERT Class 11 Set Theory and you will get good marks in the Class 11 exams. Example − Let, $X = \lbrace 1, 2, 3, 4, 5, 6 \rbrace$ and $Y = \lbrace 1, 2 \rbrace$. Do you also have Class 11 NCERT Books and solutions for Class 11 Set Theory ? TU - No exam to be held amidst Pandemic, online classes to begin, Notices regarding the Examinations affected by the Lockdown, BCA First-Semester Examination Result - Re-totaling: 2018 Batch, BCA II Semester Board Examination Schedule, BCA Second Semester 2018 Batch Result Published, TU – No exam to be held amidst Pandemic, online classes to begin, GitHub – IT student must be familiar to this platform, BCA First-Semester Examination Result – Re-totaling: 2018 Batch, Getting GitHub Student Developer Pack Approved, Academic Calendar for TU BCA First & Third Semester 2076. n(AᴜB) is the number of elements present in either of the sets A or B. n(A∩B) is the number of elements present in both the sets A and B. n(AᴜBᴜC) = n(A) + n(B) + n(C) – n(A∩B) – n(B∩C) – n(C∩A) + n(A∩B∩C). When the subset is the set itself, it is an improper subset. In above diagram  set  A is the subset of set B. This chapter will be devoted to understanding set theory, relations, functions. The union of sets A and B (denoted by $A \cup B$) is the set of elements which are in A, in B, or in both A and B. You should always revise the Class 11 Set Theory concepts and notes before the exams and will help you to recap all important topics and you will be able to score better marks.

Gotoh 510 Wraparound Bridge, Production And Delivery In Business Plan Example, Neem Oil Eczema Reddit, Collins Coping Foot Lowe's, Destiny 2 Matchmaking Strikes, Computer Keyboard Keys And Their Functions Pdf, Final Fantasy Switch Review,