Questions by yweimann - Page 33

The scientists wrote that being the first to develop nuclear weapons had given the U.S. certain responsibilities. What were those responsibilities? The text: The war has to be brought speedily to asuccessful conclusion and attacks by atomicbombs may very well be an effective method ofwarfare. We feel, however, that such attacks onJapan could not be justified, at least not unless. . . Japan were [first] given an opportunity tosurrender.The development of atomic power will providenations with new means of destruction. The atomicbombs at our disposal represent only the first stepin this direction. There is almost no limit to thedestructive power which will become availablein the course of their future development. Thus anation which [first uses them] may have to bearthe responsibility of opening the door to an era ofdevastation on an unimaginable scale.If after this war [rival powers are allowed] to bein uncontrolled possession of these new means ofdestruction, the cities of the United States as wellas the cities of other nations will be in continuousdanger of sudden annihilation*. All the resourcesof the United States, moral and material, mayhave to be mobilized to prevent . . . such a worldsituation. Its prevention is at present the solemnresponsibility of the United Statessingled out byvirtue of her lead in the field of atomic power.The [advantage] which this lead gives to theUnited States brings with it the obligation ofrestraint. If we were to violate this obligation ourmoral position would be weakened in the eyes ofthe world and in our own eyes. It would then bemore difficult for us to live up to our responsibilityof bringing the unloosened forces of destructionunder control.
Problem 2 (8 points): The propositional variables, p, q, and s have the following truth assignments: p = T, q = T, s = F. Give the truth value for the following compound proposition: p (q s)Problem 3 (8 points): Define the following propositions: p: The weather is bad. q: The trip is cancelled. r: The trip is delayed. Translate the following English sentence into logical expressions using the definitions above: The weather is bad and the trip is canceled or delayed.Problem 4 (8 points): Give the inverse, converse and contrapositive for each of the following statements: If he trained hard for the race, then he finished the race.Problem 5 (8 points): Give a truth table for the following propositions: (p q) (q p)Problem 6 (8 points): Prove that the following logical expression is logically equivalent by using a truth table. (p q) p and p qProblem 7 (8 points): Prove that the following logical expression is logically equivalent by applying the laws of logic. (p (p q)) and p qProblem 8 (10 points): In the following question, the domain of discourse is a group of people. Define the following predicates: S(x): x was sick yesterday. W(x): x went to work yesterday. Translate the following English statements into a logical expression with the same meaning: Someone who was sick yesterday went to work. Everyone who was sick yesterday did not go to work. At least one person was sick yesterday. No one went to work yesterday. Everyone who did not get work yesterday was sick.Problem 9 (10 points): Determine the truth value of each expression below if the domain is the set of all real numbers. xy (x + y = 0) xy (x + y = 0) xyz (z = 3/(x - y)) xyz (z = x/y) zyx (x^2 + y^2 = z^2)Problem 10 (8 points): Use the laws of logic to prove the conclusion from the hypotheses. Give propositions and predicate variable names in your proof. The hypotheses are: If I drive on the freeway, I will see the fire. I will either drive on the freeway or take surface streets. I am not going to take surface streets. Conclude that I will see the fire.Problem 11 (8 points): Which of the following arguments are valid? Explain your reasoning. I have a student in my class who is getting an A. Therefore, John, a student in my class is getting an A. Every girl scouts who sells at least 50 boxes of cookies will get a prize. Suzy, a girl scout, got a prize. Therefore Suzy sold 50 boxes of cookies.Problem 12 (8 points): Use the laws of logic to show that x(P(x) Q(x)) implies that x Q(x) x P(x).