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By Stouffer E. B.

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It is convenient to illustrate statements by figures as it is done in set theory. Such figures are called Venn diagrams. 1. Each point inside the rectangle represents the statement: this is a flying object; the points in the grey and white circles represent respectively the statements: this is an airplane and this is a bird. These circles do not intersect since none of the known birds is an airplane and an airplane is never a bird: the conjunction of the two statements cannot be true. 32 Example (b) T: k is divisible by 2; R: k is divisible by 3.

In each case determine whether the conclusion is true or false. In every case explain why inductive reasoning did or did not result in the right conclusion. a) I have seen a lot of birds; all of them can fly. Hence, all birds can fly. b) There is nothing but sand in a desert. c) This fellow always smiles to me and praises me, so he is my friend. d) If I eat this cereal, I will become a famous basketball player. e) This teacher is mean: he gave me a low mark. f) All bad movies are produced in Hollywood.

Visually compare segments a and b presented in Figure 1 (in each of the four cases). Then use a ruler or a compass to check your suggestion. What would you conclude based on this observation? b a b b a a b a (i) (ii) (iii) (iv) Figure 1 18. 2 ) are given. Construct the following segments: a+2c-b; 2a+2b; 2a+b – c. a+b; a – c; a+b – c; 2a; 3c; a c b Figure 2 19. Point M is located on the straight line PQ, passing through the points P and Q. a) Find MP if MQ=16cm, PQ=31cm. 8 dm. 20. A, B,C, D are four collinear points taken in consecutive order.

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A Geometrical Determination of the Canonical Quadric of Wilczynski by Stouffer E. B.


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