Chapter 1: Q5E (page 34)
Use a truth table to verify the distributive law.
The given distributive law can be verified using truth tables. Prepare the truth table for every statement and also take different values ofp, qandrsuch as every possible combination ofTandFto check the result for their verification
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
What is the value of x after each of these statements is encountered in a computer program, if x = 1 before the statement is reached?
a) if then
b) if OR then
c) if AND then
d) if XOR then
e) if x < 2 then
You can upgrade your operating system only if you have a 32-bit processor running at 1 GHz or faster, at least 1 GB RAM, and 16 GB free hard disk space, or a 64- bit processor running at 2 GHz or faster, at least 2 GB RAM, and at least 32 GB free hard disk space. Express you answer in terms of u: “You can upgrade your operating system,” b32: “You have a 32-bit processor,” b64: “You have a 64-bit processor,” g1: “Your processor runs at 1 GHz or faster,” g2: “Your processor runs at 2 GHz or faster,” r1: “Your processor has at least 1 GB RAM,” r2: “Your processor has at least 2 GB RAM,” h16: “You have at least 16 GB free hard disk space,” and h32: “You have at least 32 GB free hard disk space.”
Write each of these statements in the form “if p, then q” in English. [Hint: Refer to the list of common ways to express conditional statements provided in this section.]
a) I will remember to send you the address only if you send me an e-mail message.
b) To be a citizen of this country, it is sufficient that you were born in the United States.
c) If you keep your textbook, it will be a useful reference in your future courses.
d) The Red Wings will win the Stanley Cup if their goalie plays well.
e) That you get the job implies that you had the best credentials.
f ) The beach erodes whenever there is a storm.
g) It is necessary to have a valid password to log on to the server.
h) You will reach the summit unless you begin your climb too late.
An explorer is captured by a group of cannibals. There aretwo types of cannibals-those who always tell the truthand those who always lie. The cannibals will barbecuethe explorer unless he can determine whether a particular cannibal always lies or always tells the truth. He isallowed to ask the cannibal exactly one question.
a) Explain why the question "Are you a liar?" does notwork.
b) Find a question that the explorer can use to determinewhether the cannibal always lies or always tells thetruth.
A says “We are both knaves” and B says nothing. Exercises 24–31 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 (called normals by Smullyan [Sm78]) who can either lie or tell the truth. You encounter three people, A, B, and C. You know one of these 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 other two is. For each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. When there is no unique solution, list all possible solutions or state that there are no solutions.
A says “I am the knight,” B says “A is telling the truth,” and C says “I am the spy.”
What do you think about this solution?
We value your feedback to improve our textbook solutions.
