Chapter 3
Section 3.1
1. a. 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025.
c. 64, 32, 16, 8, 4, 2, 1, 1/2, 1/4, 1/8.
e. 1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34, 34/55, 55/89.
2. a. Basis: 1 ∈ S; Induction: If x ∈ S, then x + 2 ∈ S.
c. Basis: –3 ∈ S; Induction: If x ∈ S, then x + 2 ∈ S.
e. Basis: 1 ∈ S; Induction: If x ∈ S, then ( + 1)2 ∈ S.
3. a. Basis: 4, 3 ∈ S. Induction: If x ∈ S, then x + 3 ∈ S.
4. a. Basis: 0, 1 ∈ S; Induction: If x ∈ S, then x + 4 ∈ S.
c. Basis: 2 ∈ S; Induction: If x ∈ S, then x + 5 ∈ S.
5. 4 = 3 ∪ {3} = 2 ∪ {2} ∪ {3} = 1 ∪ {1} ∪ {2} ∪ {3} = 0 ∪ {0} ∪ {1} ∪ {2} ∪ {3} = ∅ ∪ {0} ∪ {1} ∪ {2} ∪ {3} = {0, 1, 2, 3}.
6. a. Basis: b ∈ S. Induction: If x ∈ S, then axc ∈ S.
c. Basis: a ∈ S. Induction: If x ∈ S, then aax ∈ S.
e. Basis: ...
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