2. Let N be the set of all positive integers, and S = N x N, (namely, S = [(x, y) I x, y ∈ N]). Show that there is a bijection (one-one and onto) function f :S → N, or show that no such function exists.

6. The girth of a graph G is the length of the shortest cycle in G. Let G be a simple graph with y vertices, e edges, and girth g. It is known that if G is planar, then e . Let K5 be a complete graph with 5 vertices, K5and K3,3 be a complete bipartite graph with 3 vertices in each partition. Draw Ks and K3,3, and show that they are not planar.

2. Let N be the set of all positive integers, and S = N x N, (namely, S = [(x, y) I x, y ∈ N]). Show that there is a bijection (one-one and onto) function f :S → N, or show that no such function exists.

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