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Laws of Algebra of Set
Laws of algebra of set THEOREM 1 (Idempotent Laws) For any set A (i) A ∪ A = A (ii) A ∩ A = A PROOF (i) A ∪ A= { x : x ∈ A or x ∈ A} ={x : x ∈ A} = A (ii) A ∩ A = {x : x…
Intersection of Sets
Intersection of sets Let A and B be two sets. The intersection of A and B is the set of all those elements that belongs to both A and B. See in Fig(v) shaded region show A∩B We denote A intersection B by notation “A ∩ B” Thus A∩B = { x : x ∈…
Intervals as Subsets of R
Intervals as subsets of R 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] = {…
Ordered Pairs and Equality of an Ordered Pairs
Ordered pairs An ordered pairs consists of two objects or elements in a given fixed order. For example, if A and B are any two sets, then by an ordered pair of elements we mean a pair (a, b) in that order, where a ∈ A, b ∈…
Macroscopic and Microscopic Approaches | Concept of continuum
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…