Question 9: Let S be a set consisting of 19 two-digit integers. Thus, each element of S belongs to the set 10,11,...,99]. Us the Pighoe Priniple to prove tha thisSs two istint elemems and y, such that the sum of the two digits of r is equal to the sum of the two digits of y. Question 10: Let S be a set consisting of 9 people. Every person which is an integer with 1 K age(x) in S has an age age(x), 60. .Assume that there are two people in S having the same age. Prove that there exist two subsets A and B of S such that (i) both A and B are non-empty, (ii) AnB-0, and (iii) age(x)- age(z). . Assume that all people in S having different ages. Use the Pigeonhole Principle to prove that there exist two subsets A and B of S such that) both A and B are non-empty, and(ii) EA age-XreB age(r) Assume that all people in S having different ages. Prove that there exist two subsets A and B of S such that (i) both A and B are non-empty, (ii) AnB-, andi)