Complete Test Bank Discrete Mathematics and Its Applications 8th Edition Rosen Test Bank Printed PDF,Test Bank Directly From The publisher,100% Verified Answers.COVERS ALL CHAPTERS.Download Immediately After theOrder 1 / 4
463 Test Bank Questions for Chapter 1 What is the negation of the propositions in 1{4?
1.Abby has more than 300 friends on Facebook.
2.Alissa owns more quilts than Federico.
3.A messaging package for a cell phone costs less than $20 per month.
4.4:5 + 2:5 = 6
In questions 5{9, determine whether the proposition is TRUE or FALSE.
5.1 + 1 = 3 if and only if 2 + 2 = 3.
6.If it is raining, then it is raining.
7.If 1<0, then 3 = 4.
8.If 2 + 1 = 3, then 2 = 31.
9.If 1 + 1 = 2 or 1 + 1 = 3, then 2 + 2 = 3 and 2 + 2 = 4.
10.Write the truth table for the proposition:(r! :q)_(p^ :r).
11.(a)
(b)p; q;:, and the connective_that has this
truth table.
p:p?
T T F T F F F T T F F F 12.Find a proposition with three variablesp,q, andrthat is true whenpandrare true andqis false, and false otherwise.
13.Find a proposition with three variablesp,q, andrthat is true when at most one of the three variables is true, and false otherwise.
14.Find a proposition with three variablesp,q, andrthat is never true.
15.Find a proposition using onlyp; q;:, and the connective_with the truth table
at the right.
p:p?
T T F T F T F T T F F F In 16{17, use the conditional-disjunction equivalence to nd an equivalent compound proposition that does not involve conditions.
16.:p!q
17.p!(p^q) 18.Determine whetherp!(q!r) andp!(q^r) are equivalent.
19.Determine whetherp!(q!r) is equivalent to (p!q)!r.
20.Determine whether (p!q)^(:p!q)q.
21.Write a proposition equivalent top_ :qthat uses onlyp; q;:, and the connective^.
22.Write a proposition equivalent to:p^ :qusing onlyp; q;:, and the connective_. 2 / 4
464Test Bank Questions and Answers 23.Prove that the proposition \if it is not hot, then it is hot" is equivalent to \it is hot."
24.Write a proposition equivalent top!qusing onlyp; q;:, and the connective_.
25.Write a proposition equivalent top!qusing onlyp; q;:, and the connective^.
26.Prove thatp!qand its converse are not logically equivalent.
27.Prove that:p! :qand its inverse are not logically equivalent.
28.Determine whether the following two propositions are logically equivalent:p_(q^r);(p^q)_(p^r).
29.Determine whether the following two propositions are logically equivalent:p!(:q^r);:p_ :(r!q).
30.Prove that (q^(p! :q))! :pis a tautology using propositional equivalence and the laws of logic.
31.Determine whether this proposition is a tautology: ((p!q)^ :p)! :q.
32.Determine whether this proposition is a tautology: ((p! :q)^q)! :p.In 33{39, write the statement in the form \If: : :, then: : :." 33.xis even only ifyis odd.
34.AimpliesB.
35.It is hot whenever it is sunny.
36.To get a good grade it is necessary that you study.
37.Studying is sucient for passing.
38.The team wins if the quarterback can pass.
39.You need to be registered in order to check out library books.
40.Write the contrapositive, converse, and inverse of the following: If you try hard, then you will win.
41.Write the contrapositive, converse, and inverse of the following: You sleep late if it is Saturday.In 42{44 write the negation of the statement. (Don't write \It is not true that: : :.") 42.It is Thursday and it is cold.
43.I will go to the play or read a book, but not both.
44.If it is rainy, then we go to the movies.
45.Explain why the negation of \Al and Bill are absent" is not \Al and Bill are present." 46.Usingcfor \it is cold" anddfor \it is dry," write \It is neither cold nor dry" in symbols.
47.Usingcfor \it is cold" andrfor \it is rainy," write \It is rainy if it is not cold" in symbols.
48.Usingcfor \it is cold" andwfor \it is windy," write \To be windy it is necessary that it be cold" in symbols.
49.Usingcfor \it is cold,"rfor \it is rainy," andwfor \it is windy," write \It is rainy only if it is windy and cold" in symbols.
50.Expressrdin English, whereris \it is rainy" anddis \it is dry." 51.Translate the given statement into propositional logic using the propositions provided: On certain highways in the Washington, DC metro area you are allowed to travel on high occupancy lanes during rush hour only if there are at least three passengers in the vehicle. Express your answer in terms ofr:\You are traveling during rush hour."t:\You are riding in a car with at least three passengers." andh:\You can travel on a high occupancy lane." 52.A set of propositions isconsistentif there is an assignment of truth values to each of the variables in the propositions that makes each proposition true. Is the following set of propositions consistent?The system is in multiuser state if and only if it is operating normally.If the system is operating normally, the kernel is functioning.The kernel is not functioning or the system is in interrupt mode.If the system is not in multiuser state, then it is in interrupt mode.The system is in interrupt mode.
53.What Boolean search could you use to look for web pages about U.S. national forests not in Alaska or Hawaii? 3 / 4
Chapter 1 Test Bank465 54.On the island of knights and knaves you encounter two people,AandB. PersonAsays \Bis a knave." PersonBsays \We are both knights." Determine whether each person is a knight or a knave.
55.On the island of knights and knaves you encounter two people,AandB. PersonAsays \Bis a knave." PersonBsays \At least one of us is a knight." Determine whether each person is a knight or a knave.Questions 56{58 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies who can either tell the truth or lie. You encounter three people,A, B, andC. You know one of the three people is a knight, one is a knave, and one is a spy. Each of the three people knows the type of person each of the other two is. For each of these situations, if possible, determine whether there is a unique solution, list all possible solutions or state that there are no solutions.
56.Asays \I am not a knight,"Bsays \I am not a spy," andCsays \I am not a knave." 57.Asays \I am a spy,"Bsays \I am a spy" andCsays \Bis a spy." 58.Asays \I am a knight,"Bsays \I am a knave," andCsays \I am not a knave." Find the output of the combinatorial circuits in 59{60.
59.pqr 60.pqqr Construct a combinatorial circuit using inverters, OR gates, and AND gates, that produces the outputs in 61{62 from input bitsp; qandr.
61.(:p^ :q)_(p^ :r) 62.((p_ :q)^r)^((:p^ :q)_r) Determine whether the compound propositions in 63{64 are satisable.
63.(:p_ :q)^(p!q)
64.(p!q)^(q! :p)^(p_q)
In 65{67 suppose thatQ(x) is \x+ 1 = 2x," wherexis a real number. Find the truth value of the statement.
65.Q(2)
66.8x Q(x) 67.9x Q(x) In 68{75P(x; y) means \x+ 2y=xy," wherexandyare integers. Determine the truth value of the statement.
68.P(1;1)
69.P(0;0)
70.9y P(3; y) 71.8x9y P(x; y) 72.9x8y P(x; y) 73.8y9x P(x; y) 74.9y8x P(x; y) 75.:8x9y:P(x; y)
- / 4