MAD 2104 Midterm: MAD 2104 FIU Exam 510k
Document Summary
1a) [20pts each] suppose k integers are chosen from the rst eleven positive integers. Show that if k 8, then some pair of the chosen integers has a sum equal to 12. 1b) find the smallest value of k that makes the conclusion true. 2a) [15pts each] a coin is tossed 10 times, where each toss comes up heads or tails. 3a) [15pts each] let r = {(1, 2), (3, 1), (2, 1), (1, 3), (2, 2)} be a relation on a = {1, 2, 3}. Remarks and answers: the average among the top 20 students was about 65 / 100. Here is a rough scale for the quiz, based mainly on that average: 1a) the pigeons are the k chosen integers. The pigeonholes are the 6 sets {1, 11}, {2, 10}, By the php (since k > 6), some set contains two of the chosen numbers (and it is obviously not the last set), and those sum to 12.
