1. Let G1, G2, . . . , Gm be (not necessarily distinct) complete subgraphs of Kn, such that each 01 contains at most n 1 vertices and such that each edge of Kn belongs to the same number A (2 1) of Gi's. Prove the following statements. (a) Each vertex of Kn belongs to at least A + 1 of Gi's. (b) Let M be the n X m matrix such that M(i,j) : 1 if the vertex 1' of Kn is contained in G]- and 0 otherwise. Then rk:(MMT) : n. (c)1fn Z 2, then m 2 n