Discrete Mathematics教学习题（华南理工）Tutorial04-Answer.pdfVIP

Discrete Mathematics I (Semester 2, 2013-2014) Tutorial 04 - Answer Refer to Chapter 2.1 and 2.2 Date: March-2014 2 1. List the members of the set {x | x is an integer such that x = 2}. Answer: ∅ 2. Use set builder notation to give a description of each of these sets. a) {0, 3, 6, 9, 12} b) {-3, -2, -1, 0, 1, 2, 3} Answer: a) {x | x = 3n, where n is 0, 1, 2, 3, 4 } b) {x | x is a positive integer and |x| ≤ 3} 3. Determine whether each of these pairs of sets are equal. a) {1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} b) {{1}}, {1, {1}} c) ∅, {∅} Answer: (a) Yes, for they have the same element (b) No, {1} is a set, so {1,{1}} has two elements, while {{1}} has only one (c) No, ∅ is a element but {∅} is a set. 4. For each of the following sets, determine whether 2 or {2} is an element of that set. a) {x ∈ R | x is an integer greater than 1} b) {x ∈ R | x is the square of an integer} c) {2,{2}} d) {{2},{{2}}} e) {{2},{2,{2}}} f) {{{2}}} Discrete Mathematics I – Tutorial 4