机械工业出版社离散数学英文版部分答案.docVIP

1.1: P17 Ex8 a): If you have the flu, then you miss the final exam. Ex 8 c): if you miss the final exam, then you do not pass the course. Ex 8 e): it is either the case that if you have the flu then you do not pass the course or the case that if you miss the final exam then you do not pass the course. Ex12: T F T F Ex28: P q a) c) e) f) F F F T T F T T T F T T F F F F T T T F F T Ex36: a) x=2 c) x=2 e) x=2 Ex48: a) r(?p b) (r(p)(q c) ?r(?q d) (?p(r)(q Ex52: This system is consistent. We use L, Q, N, and B to stand for the basic operations here, “ the file system is locked”, “New messages will be queued”, “the system is functioning normally”, and “New messages will be sent to the message buffer”, respectively. Then the given specifications are ?L(Q, ?L?N, ?Q(B, ?L(B, ?B. If we want consistency, then we had better have B=F, L=T, Q=T, N=F. Ex64: a) John did; b) Carlos did. 1.2: P28 Ex8 a) Kwame will not take a job in industry and will not go to graduate school. c) James is not young, or he is not strong. Ex10: P Q a) c) F F T T F T T T T F T T T T T T Ex26: ?p((q(r) (?p((q(r) (?p((?q(r)?(??q((p(r)?(?q((p(r) Ex40: p ( q (?r 1.3: P47 Ex8 a) If an animal is a rabbit, then that animal hops. (Alternatively, every rabbit hops) c) There exists an animal such that if it is a rabbit, then it hops. Ex12 a) True c) False e)False g)False Ex20 a) P(-5)?(?P(-3)?(?P(-1)?(?P(1)?( P(3)?( P(5)? c) P(-5)?(?P(-3)?(?P(-1)?(?P(3)?(?P(5) e) (?P(1)?( ?P(3)?( ?P(5))? (??P(-1)?(?P(-3)?(?P(-5)) Ex28 Let R(x)=”x is in the correct place”, E(x)=”x is in excellent condition”, T(x)=”x is a tool” a) ( x ?R(x) c) (x (R(x) (?E(x)) e)?( x (T(x) (?R(x)?(E(x)) Ex44: For example, we can take P(x) to mean that x is an even number and Q(x) to mean that x is a multiple of 3, and we can find they are not logically equivalent. Ex53: T F T 1.4: P58 Ex4 a) Some student in your class has taken some computer science course. c) Every student in your class has taken at least on