Dse 2007 Doubts

[arpit bansal]

Can anybody tell me the theory behind Q-44,45,46

[arpit bansal]

tell me how to do this type of questions.
http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/30_jun_2007_option_a.pdf

[onionknight]

44.) You are supposed to find the intersection of sets starting from (-2,2), (-1.5,1.5).....upto (-1-1/n,1+1/n) where n approaches infinity. As n approaches infinity 1/n approaches 0 but it won't exactly be zero, thus -1-1/n is a number infinitesimally bigger than -1 and 1+1/n is a number infinitesimally bigger than 1. Thus, the set [-1,1] will be contained in all these sets and also in their intersection.

45.) You are supposed to find the union of sets starting from [0,0], [-1/2,1/2]..... upto [-1+1/n,1+1/n] where n approaches infinity. As n approaches infinity 1/n approaches 0 but it won't exactly be zero, thus -1+1/n is a number infinitesimally bigger than -1 and 1-1/n is a number infinitesimally smaller than 1. Thus, the union will contain all values between -1 and 1 without containing the border values -1 and 1. Answer (-1,1)

[onionknight]

46.) Not the best way to do it but it works. Let n be 2. Let the point x be (0,0). Draw a square of side a in the first quadrant with its bottom left vertex located at the origin. Now choose the points y and z on the two edges of the square located in the first quadrant. Here, d(x,y)=d(x,z)=a irrespective of where the two points are located on the edges. d(y,z) can be anything between 0 and a. So d(x,z) <= d(x,y)+ d(y,z)