Reference no: EM131587224

Question: 1. Prove that if A ⊆ B, then B¯ ⊆ A¯. Do this once using Venn diagrams and once using element notation.

2. Prove that if a ≡ b (mod n) and c ≡ d (mod n), then a-c ≡ b-d (mod n).

3. The distance between two vertices x and y of a graph, denoted d(x,y), is the length of the shortest path joining x and y. If x,y,z are vertices of graph G, is it always true that d(x,y)+d(y,z) ≥ d(x,z)? Give a proof or a counterexample.