----!!!!!-------> EXAM on Wed. Feb 15th moved to ROOM CLS 1001 <-----!!!!!----- CS 201-31, Discrete Structures, Spring 2001, Assignment 3 Solution Section 2.1, page 70: 4d) {..., -5, -3, -1, 1, 3, 5, 7, ...}. 4e) { x : x = 10k, k ∈ N }. 4f) { } or ∅ , but NOT {∅ } Section 2.7, page 96: Prove the following statement: If x is odd, then x2 is odd. Proof: (1) Assume x is odd. (2) ∴ x = 2k + 1, for some k ∈ Z. (3) ∴ x2 = (2k + 1) 2 . (4) ∴ x2 = 4k2 + 4k + 1. (5) ∴ x2 = 2(2k2 + 2k) + 1. (6) Since m = 2k2 + 2k ∈ Z , x2 can be written in the form x2 = 2m + 1, for some m ∈ Z. (7) ∴ x2 is odd. PROOF COMPLETE. Section 2.2, page 73: 4) B = {a, b, c, d, e}. List all subsets of B having exactly 2 elements {a, b}, {a, c}, {a, d}, {a, e}, {b, c}, {b, d}, {b, e}, {c, d}, {c, e}, {d, e} 10 of them. 6a) Is every subset of a finite set finite? This is true. Need to show: If A ⊆ B and B is fini...