Let n, k EN and define the family of graphs G, (V, Ek) on the vertex set V,= (1,2,... ,n} and with edge set Enk= {(i,j) E V, x V: ij (mod k)}. In other words, two vertices i and j are adjacent if they are congruent modulok. (a) Draw G12 and G73 and show they are both disconnected. (b) Show that G is connected if and only if k 1. (c) Show that Gk is the empty graph if and only if n

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.