P1 [5+10=15 points) Pigeonhole Principle P1a) 105 a) Suppose that you have an array of X numbers where X is your parameter for Pla. What is the largest number n such that you are guaranteed to have either an increasing or a decreasing subsequence of length n in your array? P2b)10,10 b) How many ordered pairs of integers (a,b) are needed to guarantee that there are two ordered pairs (ai, b) and (a2, b2) such that a1 = 12 mod A and b = b2 mod B where A and B are your parameters for P2b? P1 [5+10=15 points) Pigeonhole Principle P1a) 105 a) Suppose that you have an array of X numbers where X is your parameter for Pla. What is the largest number n such that you are guaranteed to have either an increasing or a decreasing subsequence of length n in your array? P2b)10,10 b) How many ordered pairs of integers (a,b) are needed to guarantee that there are two ordered pairs (ai, b) and (a2, b2) such that a1 = 12 mod A and b = b2 mod B where A and B are your parameters for P2b