Plus One | Maths | Chapter 1 | Sets | Exam Preparation | Malayalam

Plus one, Mathematics, Chapter 1. Sets, problems solved. /playlist/PLiOs_9vgOde0ReRn00u6IA3h9mFa-O4x2 Introduction. Different types of sets. Chapter 1 SETS 1.1 Introduction 1.2 Sets and their Representations In everyday life, we often speak of collections of objects We give below a few more examples of sets N : the set of all natural numbers Z : the set of all integers Q : the set of all rational numbers R : the set of real numbers Z+ : the set of positive integers Q+ : the set of positive rational numbers, and R+ : the set of positive real numbers. We shall say that a set is a well-defined collection of objects. There are two methods of representing a set : (i) Roster or tabular form (ii) Set-builder form. 1.5 Equal Sets 1.6 Subsets Consider the sets : X = set of all students in your school, Y = set of all students in your class. A ⊂ B if a ∈ A ⇒ a ∈ B We read the above statement as “A is a subset of B if a is an element of A implies that a is also an element of B”. If A is not a subset of B, we write A ⊄ B. The set of irrational numbers, denoted by T, is composed of all other real numbers. Thus T = {x : x ∈ R and x ∉ Q}, N ⊂ Z ⊂ Q, Q ⊂ R, T ⊂ R, N ⊄ T. 1.7 Power Set Definition 5 The collection of all subsets of a set A is called the power set of A. It is denoted by P(A). In P(A), every element is a set. 1.8 Universal Set 1.10 Operations on Sets 1.10.1 Union of sets Let A and B be any two sets. A ∪ B = { x : x ∈A or x ∈B } Some Properties of the Operation of Union (i) A ∪ B = B ∪ A (Commutative law) (ii) ( A ∪ B ) ∪ C = A ∪ ( B ∪ C) (Associative law ) (iii) A ∪ φ = A (Law of identity element, φ is the identity of ∪) (iv) A ∪ A = A (Idempotent law) (v) U ∪ A = U (Law of U) 1.10.2 Intersection of sets A ∩ B = {x : x ∈ A and x ∈ B}. The intersection of two sets A and B A ∩ B = {x : x ∈ A and x ∈ B} If A and B are two sets such that A ∩ B = φ, then A and B are called disjoint sets. Some Properties of Operation of Intersection (i) A ∩ B = B ∩ A (Commutative law). (ii) ( A ∩ B ) ∩ C = A ∩ ( B ∩ C ) (Associative law). (iii) φ ∩ A = φ, U ∩ A = A (Law of φ and U). (iv) A ∩ A = A (Idempotent law) (v) A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) (Distributive law ) i. e., 1.10.3 Difference of sets A – B = { x : x ∈ A and x ∉ B } 1.11 Complement of a Set Some Properties of Complement Sets 1. Complement laws: (i) A ∪ A′ = U (ii) A ∩ A′ = φ 2. De Morgan’s law: (i) (A ∪ B)´ = A′ ∩ B′ (ii) (A ∩ B )′ = A′ ∪ B′ 3. (A′ )′ = A 4. Laws of empty set and universal set φ′ = U and U′ = φ. (ii) n ( A ∪ B ) = n ( A ) + n ( B ) – n ( A ∩ B ) ... (2) n ( A ∪ B) = n ( A – B) + n ( A ∩ B ) + n ( B – A ) (iii) If A, B and C are finite sets, then n ( A ∪ B ∪ C ) = n ( A ) + n ( B ) + n ( C ) – n ( A ∩ B ) – n ( B ∩ C) – n ( A ∩ C ) + n ( A ∩ B ∩ C ) Summary This chapter deals with some basic definitions and operations involving sets. These are summarised below: A set is a well-defined collection of objects. A set which does not contain any element is called empty set. A set which consists of a definite number of elements is called finite set, otherwise, the set is called infinite set. Two sets A and B are said to be equal if they have exactly the same elements. A set A is said to be subset of a set B, if every element of A is also an element of B. Intervals are subsets of R. A power set of a set A is collection of all subsets of A. It is denoted by P(A). The union of two sets A and B is the set of all those elements which are either in A or in B. The intersection of two sets A and B is the set of all elements which are common. The difference of two sets A and B in this order is the set of elements which belong to A but not to B. The complement of a subset A of universal set U is the set of all elements of U which are not the elements of A. For any two sets A and B, (A ∪ B)′ = A′ ∩ B′ and ( A ∩ B )′ = A′ ∪ B′ If A and B are finite sets such that A ∩ B = φ, then n (A ∪ B) = n (A) + n (B). If A ∩ B ≠ φ, then n (A ∪ B) = n (A) + n (B) – n (A ∩ B) tags Sets Mathematics Mathematics KERALA Class 11 Sets Set Concept Maths class 11 Class 11 XI XI Maths malayalam sets stes maths plus one malayalam Class 11 XI Maths CBSE Sets Part 1 malayalam plus one,chapter 1 maths malayalam kerala plus one kerala plus one maths plus one maths sets malayalam sets chapter sets videos plus one ncert ncert ncert plus one maths study online maths study material maths entrance +1 TUITION class room video sets class 11 malayalam set class 11 malayalam jm learn sets maths class 11 malayalam sets stes maths plus one malayalam plus one maths sets malayalam sets chapter sets videos plus one ncert ncert plus one +1 TUITION class room video set class 11 malayalam sets class 11 malayalam +1 maths sets plus one maths chapter 1 maths sets class 11 malayalam maths sets class 11 in malayalam

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