Rotation of Axis: Let -coordinate system be given. We rotate and and about the origin through an angle so that the new axes are and as shown in the figure. Let a point have coordinates referred to the -system of coordinates. Suppose has coordinates referred to the -coordinate system. We have to find in terms […]
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What is Geometry in Math: Geometry is one of the most ancient branches of mathematics. The Greeks systematically studied it about four centuries B.C. Most of the geometry taught in schools is due to Euclid who expounded thirteen books on the subject (300 B.C.). A French philosopher and mathematician Rene Descartes (1596-1650 A.D.) introduced algebraic
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Negation: If p is any proposition its negation is denoted by ~p, read‘not p‘. It follows from this definition that if p is true, ~p is false and ifp is false, ~p is true. The adjoining table, called the truth table, gives thepossible truth- values of p and ~p. Conjunction: The conjunction of two statements
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A compound statement of the form if p then q , also written p implies q , is called aconditional or an implication, p is called the antecedent or hypothesis and q is called theconsequent or the conclusion.A conditional is regarded as false only when the antecedent is true and consequent isfalse. In all other
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Just as operations of addition, subtraction etc., are performed on numbers, theoperations of unions, intersection etc., are performed on sets. We are already familiar withthem. A review of the main rules is given below: –Union of two sets: The Union of two sets and , denoted by , is the set of all elements,which belong
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For the sake of brevity, propositions will be denoted by the letters , etc. We give a brief list of the other symbols which will be used. Symbolic Logic Table Symbol How to be read Symbolic expression How to be read NOT or Negation Not , negation of AND or Conjunction and OR or Disjunction
For reasoning we have to use propositions. A declarative statement which may be trueor false but not both is called a proposition. According to Aristotle there could be only twopossibilities – a proposition could be either true or false and there could not be any thirdpossibility. This is correct so far as mathematics and other
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Induction:- In daily life we draw conclusions from a limited number of observations. A person gets penicillin injection once or twice and experiences reaction soon afterwards. He generalises that he is allergic to penicillin. We generally form opinions about others on the basis of a few contacts only. This way of drawing conclusions is called
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Rank of a Matrix: Let M be a non-zero matrix. If r is the number of non-zero rows when it isreduced to the reduced echelon form, then r is called the (row) rank of the matrix M. Example: Find rank the rank of matrix Solution:
Field definition math: A set S is called a field if the operations of addition ‘+ ’ and multiplication ‘. ’ on S satisfythe following properties are written in tabular form: Addition Closure for any set Commutativityfor any Associativityfor any Existence of Identityfor any such that Existence of Inversesfor any such that Distributivity for any
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