Answer Happy

Question 8 (a) Use the pigeonhole principle to show that if you randomly arrange the numbers 1-12 around a square, 3 numbers along each side of the square, that the numbers along at least one of the sides must add up to 20 or more. (b) How many friends must you have to guarantee at least 5 of them will have birthdays in the same month. Use the extended pigeonhole principle. Question 9 Let A = {2,3,4,6,9,12,18) and define a relation Ron A as follows aRb if and only if a and b have the same prime factors. (For example, 3R9 since both 3 and 9 have only the prime factor 3. But 69 since 6 has 2 and 3 as prime factors and 9 has only 3 as prime factor.) (a) Draw the directed graph of R. (b) Give the in/out degrees of 3 and 18. (c) Give the domain and range of R. (d) Determine R(6). (e) Determine M, and use M, and Boolean multiplication to find R.