Month: March 2014

Problem-32 Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms…

Problem-31 Let A={a,b,c}, B={x,y}, and C={0,1}. Find B×C×A.   Solution {(x,0, a),(x,1, a),(y,0, a),(y,1, a),(x,0, b),(x,1, b),(y,0, b),(y,1, b),(x,0, c),(x,1, c),(y,0, c),(y,1, c)}

Problem -30 Use a Venn diagram to illustrate the relationship A⊆B and B⊆C. Solution  

Problem-29 Suppose that A={5,8,9}, B={5,9}, C={8,9}, and D={8,9,10}. Determine which of these sets are subsets of which other of these sets. a) A⊆ b) B⊆ c) C⊆ d) D⊆   Solution a) A⊆ A  …

Problem- 28 Determine whether each of these pairs of sets are equal. a) {2, 2, 4, 4, 4, 6, 8, 8},{8, 6, 4, 2} b) {{2}},{2,{2}} c) ∅,{∅}   Solution…

Problem- 27 Use set builder notation to give a description of each of these sets.   a) {0,3,6,9,12} b) {−4, −3, −2, −1, 0, 1, 2, 3, 4} c) {a,…

Problem- 26 Show that each of these conditional statements is a tautology by completing the truth tables. We conclude that each of these conditional statements is a tautology because the…

Problem- 25 Use De Morgan’s laws to find the negation of the following statement. Kwame will take a job in industry or go to graduate school.   Solution   Kwame will…

Problem- 24 An explorer is captured by a group of cannibals. There are two types of cannibals – those who always tell the truth and those who always lie. The cannibals…

Problem-23 Are these system specifications consistent? “Whenever the system software is being upgraded, users cannot access the file system. If users can access the file system, then they can save…