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HW Set 1 for wed

pg 9: 1,2,3, 4,5

Set 2: 4th edition of book

pg 31: 1,2,3,4,5,9

Set 3: from Wilson graph theory

1: Construct graphs G₁, G₂ with same number of edges and vertices, which are NOT isomorphic.
5.1, 5.3, 5.4
6.1, 6.2
7.1, 7.2

Set 4: Wilson

1. Complete proof of Theorem 7.1 by proving that vertices v_i, v_i − 1 exist. Hint: this can be proved by induction on n.

2. Prove that a graph with n vertices and n − 2 edges is disconnected.

8.4, 9.3, 9.6, 9.10, 12.1, 12.3, 12.7, 13.2, 13.5

Set 5: Wilson

pg 72: 14.1, 14.2, 14.4, 14.7 (Extra credit)

Set 6: Wilson

pg 76: 15.1, 15.2, 15.4, 15.9

Set 7:

1: Let S be an infinite subset of a countable set, prove that S is countable.
2: Prove ℤ is countable.
3: Prove that ℚ is countable.
4: Prove that a countable union ∪_i ∈ IU_i, I countable, of countable sets U_i is countable.
4: Use the Cantor diagonalization argument which we used to prove that the set {0, 1}^ℕ is not countable to prove that ℝ is not countable.

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