Eight students solved 8 problems. a) It turned out that each problem was solved by 5 students. Prove that there are two students such that each problem is solved by at least one of them.b) If it turned out that each problem was solved by 4 students, it can happen that there is no pair of students such that each problem is solved by at least one of them. (Give an example.) Proposed by S. Tokarev pigeonhole principlelinear algebramatrix