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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
Complete proof of Theorem 7.1 by proving that vertices vi, vi − 1 exist. Hint: this can be proved by induction on n.
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 ∈ IUi, I countable, of countable sets Ui 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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