Macroscopic and Microscopic Approaches The behaviour of matter can be studied by two approaches 1. Macroscopic approach, 2. Microscopic approach 1. Macroscopic approach – In the macroscopic approach a certain quantity of matter is considered for study without knowing the behaviour of individual…
CLOSED INTERVALS Let a and b be two given real numbers such that a < b. Then the set of all real numbers x such that a ≤ x ≤ b is called a closed interval and is denoted by [a, b] . Thus, [a, b] = { x : x ∈ R,…
THEOREM 2 The empty set is a subset of every set. PROOF Let A be any set and ϕ be the empty set.ln order to show that ϕ ⊆ A,we must show that every element of ϕ is an element of A also. But ϕ contains no element. So, every element of ϕ…
THEOREM 1 Every set is a subset of itself. PROOF:- Let A be any set. Then, each element of A is clearly in A itself. Hence, A ⊆ A.
SUBSETS Let A and B be two sets. If every element of A is an element of B, then A is called a subset of B and B is called super set of A. A ⊆ B is read as A is subset of B B ⊃ A is read as B is super set…
TYPES OF SETS a) Empty setA set is said to be empty or null or void set if it has no element and it is denoted by Φ In Roster method is Φ denoted by { }.Example{ x : x ∈ R, x2=-2 }=Φ { x : x ∈ N, 5<x<6 }=Φ D={ x :…
REPRESENTATION OF A SET A set is often described in the following two forms. One can make use of any one of these two ways according to his/her convenience (i) Roster form or Tabular form(ii) Set-builder formLet us now discuss one by one.(i) Roster form or Tabular form:-In this form a set is described by…
What is a set? Set can be defined as the collection of well-defined object that’s all.The meaning of ” well-defined” in set is those type of collection which is not depend on choice.Like collection of beautiful women in India. Which depend on choice only and different people has different different choice. So such collection is…
Conservation of Energy In the early part of 19th century the scientist developed the concept of energy and hypothesis that it can be neither created nor destroyed ; this come to be known as the law of the conservation of energy. The first law of thermodynamics is merely one statement of this…
