If two sets contain the same elements they are said to be equal. Let $S = \lbrace 1, 2, 3\rbrace$, $n = |S| = 3$, 2. Can I download the Notes for other subjects too ? Sets can be classified into many types. Singleton set or unit set contains only one element. 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}. 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. $|X| \le |Y|$ denotes that set X’s cardinality is less than or equal to set Y’s cardinality. Example 2 − Let, $X = \lbrace 1, 2, 3 \rbrace$ and $Y = \lbrace 1, 2, 3 \rbrace$. Therefore, {1,2} ⊂ {1,2,3} and {1,2,3} ⊆ {1,2,3}. Note − The power set of an empty set is also an empty set. Notations for Sets of Numbers. The intersection of two sets is a set containing only the members that are in each set at the same time. Introduction to naive set theory Fundamental set concepts. There is a common element ‘6’, hence these sets are overlapping sets. Example − Let, $A = \lbrace 1, 2, 6 \rbrace$ and $B = \lbrace 7, 9, 14 \rbrace$, there is not a single common element, hence these sets are overlapping sets. A set is an unordered collection of different elements. 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. FORMULAS. $| P (\lbrace \emptyset \rbrace) | = 2^0 = 1$, 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 −, $\lbrack P_i \ne \lbrace \emptyset \rbrace\ for\ all\ 0 \lt i \le n \rbrack$. Set Theory is the true study of infinity. Example − If $A = \lbrace 1, 2, 6 \rbrace$ and $B = \lbrace 6, 1, 2 \rbrace$, they are equal as every element of set A is an element of set B and every element of set B is an element of set A. Benefits of Notes for Class 11 Set Theory, a) Will help you to revise all important concepts prior to the school exams of Class 11 in a timely manner. As we have already discussed, in mathematics set theory, a set is a collection for different types of objects, and collectively itself is called an object. POINTS TO KNOW. Properties of Basic Mathematical Operations, Quiz: Properties of Basic Mathematical Operations, Quiz: Multiplying and Dividing Using Zero, Quiz: Signed Numbers (Positive Numbers and Negative Numbers), Simplifying Fractions and Complex Fractions, Quiz: Simplifying Fractions and Complex Fractions, Signed Numbers (Positive Numbers and Negative Numbers), Quiz: Variables and Algebraic Expressions, Quiz: Solving Systems of Equations (Simultaneous Equations), Solving Systems of Equations (Simultaneous Equations), Quiz: Operations with Algebraic Fractions, Solving Equations Containing Absolute Value, Quiz: Linear Inequalities and Half-Planes, Online Quizzes for CliffsNotes Algebra I Quick Review, 2nd Edition. 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 intend of this article is to let us know the significance of writing within the prescribed word limit while attempting the CBSE Board Examination. Power set is denoted as $P(S)$. Previous 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. 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. In above diagram set A is the subset of set B. We believe that knowledge and experience are the two major factors that create a responsible person for the betterment of society. A set is a group of objects, numbers, and so forth. $\lbrace 1 \rbrace , \lbrace 2 \rbrace , \lbrace 3 \rbrace$, 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. Power set of a set S is the set of all subsets of S including the empty set. 1.1 Sets Mathematicians over the last two centuries have been used to the idea of considering a collection of objects/numbers as a single entity. Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. from your Reading List will also remove any This method not only helps in saving the energy and time of the students during the Class 11 Examination but also helps them to recall all the things which they have studied in less time. The symbol used to indicate “is a proper subset of” is ⊂. Also download collection of CBSE books for... Download Class 11 Set Theory assignments. 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 −, $B = \lbrace x : 1 \le x \lt 10 \ and\ (x \% 2) \ne 0 \rbrace$.