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What is Inductive Reasoning ?
Sometimes we draw conclusions based on our observations. If we observe the same results again and again, we conclude that the event always has the same outcome. We call this kind of reasoning inductive reasoning. We call a conclusion arrived at through inductive reasoning as a generalization.
Example 1 : Suppose there are 3 differently shaped triangles. If we cut off the corners of each of the triangles and patch them together, we will find that the sum of the angles of each triangle is 180°. If we do this to a large number of triangles, then we find that the sum is always 180°. We can generalize this to say that the sum of the angles of a triangle is 180°.
Example 2 : Here we have two right triangles and find and and We can generalize this to say: The side opposite the right angle of a triangle is the longest side. Sometimes generalizations can be false. We look for counterexamples to show a generalization is false.
Example 3 : Generalization: If a quadrilateral has four congruent sides, it has four congruent angles. Counterexample: We can draw a quadrilateral with four congruent sides but with unequal angles to show this is a false generalization.
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Mike, Dan, Ed, and Sy played together on a baseball team. Mike's batting average was 0.349, Dan's was 0.2, Ed's was 0.35, and Sy's was 0.299. Who had the highest batting average?
we know that log1 to any base =0 take antilog threfore a 0 =1
The digraph D for a relation R on V = {1, 2, 3, 4} is shown below (a) show that (V,R) is a poset. (b) Draw its Hasse diagram. (c) Give a total order that have R.
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Verify Liouville''s formula for y^ prime prime prime -y^ prime prime - y'' + y = 0 in [0, 1]
Example of Probability Illustration: It has been determined that the probability density function for the wait in line at a counter is specified by, In which t is the
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What do we mean by the roots of a quadratic equation ?
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