Chapter 1: Q48E (page 36)
Construct a truth table for the logical operator NOR.
For NOR logical operator, the output is true if both the inputs such as of pand q are false. Use this concept for the construction of truth table for NOR.
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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.”
How many rows appear in a truth table for each of these compound propositions?
a)\(p \to \neg p\)
b)
c)
d) \((p \wedge r \wedge t) \leftrightarrow (q \wedge t)\)
To use the wireless network in the airport you must pay the daily fee unless you are a subscriber to the service. Express your answer in terms of w: “You can use the wireless network in the airport,” d: “You pay the daily fee,” and s: “You are a subscriber to the service.”
Construct a truth table for
Suppose that Smartphone A has MB RAM and GB ROM, and the resolution of its camera is MP; Smartphone B has MB RAM and GB ROM, and the resolution of its camera is MP; and Smartphone C has MB RAM and GB ROM, and the resolution of its camera is MP. Determine the truth value of each of these propositions
a) Smartphone Bhas the most RAM of these three smartphones.
b) Smartphone C has more ROM or a higher resolution camera than Smartphone
B
c) Smartphone B has more RAM, more ROM, and a higher resolution camera than SmartphoneA
d) If Smartphone B has more RAM and more ROM than Smartphone C, then it also has a higher resolution camera.
e) Smartphone A has more RAM than Smartphone B if and only if Smartphone B has more RAM than Smartphone A
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