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What are the Basic Elements of Reasoning ?
There are four basic elements used in geometry. If we say studying geometry is like building a house, then these elements are like different types of materials. Logical methods of reasoning can bind these elements together and allow us to build on our foundation to create a wide range of structures. The four basic elements are the following:
1. Undefined Term : A word is so fundamental that it cannot be satisfactorily be defined. However, undefined terms can be described. Example: point, line, and plane.
2. Definition : A definition clearly states the meaning of a term or an idea. The reverse of a definition must be also true. Definitions begin by identifying the term to be defined. We state the characteristics of the term which have been previously defined or are commonly understood. Defined terms are words or symbols people use which refer to geometric figures and relationships. Example: segment, ray and angle.
3. Postulate (sometimes referred to as an "axiom") : A postulate is a statement that is based on experience and people take for granted.
4. Theorem : A theorem is a generalization which can be proven true by means of other true statements.
Disjointed Sets or Mutually Exclusive Two sets are said to be mutually or disjointed exclusive whether they have no elements in common. Sets P and R underneath are disjointed
(a) Find the curve on the surface z=x 3/2 joining the points(x,y,z)=(0,0,0) and (1,1,1) has the shortest arc lenght? (b) Use a computer to produce a plot showing the surface an
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prove that every non-trivial ingetral solution (x,y,z)of the diophantine equation Xsquare +Ysquare=Zsquare satisfies gcd(x,y)=gcd(x,z)=gcd(y,z)
Find the area of shaded region of circle of radius =7cm, if ∠AOB=70 o , ∠COD=50 o and ∠EOF=60 o . (Ans:77cm 2 ) Ans: Ar( Sector AOB + Sector COD + Sector OEF) = 7
A firm is manufacturing 45,000 units of nuts. The probability of having a defective nut is 0.15 Compute the given i. The expected no. of defective nuts ii. The standard an
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Determine the linear approximation for f(x)= sin delta at delta =0
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Integration We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative
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