Category: Algebra

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…

Problem-22 Complete the truth table for each of these compound propositions. a) p→(¬q∨r) b) ¬p→(r→q) c) (p→q)∧(¬p→r) d) (p↔q)∨(¬q↔r) e) (¬p↔¬q)↔(q↔r)   Solution   a) p→(¬q∨r)   p q r…

Problem-21 State the converse, contrapositive, and inverse of each of these conditional statements. a) If it snows tonight, then I will stay at home. b) I come to class whenever…

Problem-20 Let p, q, and r be the propositions p: You have the flu. q: You miss the final examination. r: You pass the course. Express each of these propositions as…

Problem-19 Which of these are propositions? What is the truth value of those that are propositions? a) Answer this question. b) What time is it? c) There are no black flies in…