Homework 1 copy

Homework 1 copy - , 5)-graph. (6) Is there a simple graph...

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HOMEWORK 1 8 PROBLEMS DUE: WEDNESDAY, JANUARY 19, 2011 (1) Let A = { 3 , 4 , 5 } ,B = { 3 , 4 } ,C = { 4 } . Find D = A 4 B 4 C . (2) Suppose 70% of Californians like cheese, 80% like apples and 10% like neither. What percentage of Californians like both cheese and apples? (3) Use the Principle of Mathematical Induction to prove that for n N , n 3 - n is always divisible by 3. (4) Find a surjective function from N to Z . Find an injective function from Z to N . (5) Write an explicit description of the edgemap for the complete bipartite (3
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Unformatted text preview: , 5)-graph. (6) Is there a simple graph on 6 vertices such that the vertices all have distinct degree? If not, why not? If so, draw one. (7) Let G be a k-regular graph, where k is an odd number. Prove that the number of edges in G is a multiple of k . (8) Prove that it is impossible to have a group of nine people at a party such that each one knows exactly ve of the others in the group....
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