TheMathWorld

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…

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…