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1、P.161.14.f) If I did not buy a lottery ticket this week, then Idid not winthe million dollar jackpot on Friday.g) I did not buy a lottery ticket this week, and I did not win the million dollar jackpot on Friday.h ) Either I did not buy a lottery ticket this week, or else I did buy one and won the mi
2、llion dollar jackpot on Friday.10.a) r qb) p q rc) r pd) p q r e) (p q) r f) r ( q p)20.a) If I am to remember to send you the address, then you will have to send me an e-mail message.(This has been slightly reworded so that the tenses make more sense.)b) If you were born in the United States, then
3、you are a citizen of this country.c) If you keep your textbook, then it will be a useful reference in your future courses.(The word then is understood in English, even if omitted.)d) If their goaltender plays well, then the Red Wings will win the Stanley Cup.e) If you get the job, then you had the b
4、est credentials.f) If there is a storm, then the beach erodes.g) If you log on to the server, then you have a valid password.h) If you dont begin your climb too late, then you will reach the summit.33.c) pqr(p q) (p r) TTTTTTFTTFTTTFFTFTTTFTFTFFTTFFFTP.261.28.a) Kwame will not take a job in industry
5、 and he will not go to graduate school.b) Yoshiko doesnt know Java or she doesnt know calculus.c) James is not young or he is not strong.d) Rita will not move to Oregon and she will not move to Washington.10.a) pqppqp(pq)p(pq)qTTFTFTTFFTFTFTTTTTFFTFFTc)pqp qp(p q)p(p q) qTTTTTTFFFTFTTFTFFTFT12.a) As
6、sume the hypothesis is true. Then p is false. Since pq is true, we conclude that q must be true.Here is a more algebraic solution:p (p q)q p(p q)q p(p q)q p(p q)q (p q)(p q) Tc) Assume the hypothesis is true. Then p is true, and since the second part of the hypothesis is ture, we conclude that q is
7、also true, as desired.24.pqrp qp r(p q) (p r)q rp (q r)TTTTTTTTTTFTFTTTTFTFTTTTTFFFFFFFFTTTTTTTFTFTTTTTFFTTTTTTFFFTTTFT30.pqrp qp rq r(p q)(p r)(p q)(p r) (q r)TTTTTTTTTTFTFTFTTFTTTTTTTFFTFFFTFTTTTTTTFTFTTTTTFFTFTTFTFFFFTFFT51.(p p) q )(p p) q )9.77. The graph is planar.a d e cf b20. The graph is no
8、t homeomorphic to K3,3, since by rerouting the edge between a and h we see that it is planar.22. Replace each vertex of degree two and its incident edges by a single edge. Then the result is K3,3 : the parts are a,e,i and c,g,k. Therefore this graph is homeomorphic to K3,3.23. The graph is planar.25
9、. The graph is not planar.9.83. 3 A F BC ED8. 39. 210. 417.time slot 1: Math 115, Math 185;time slot 2: Math 116, CS 473;time slot 3: Math 195, CS 101;time slot 4: CS 102time slot 5: CS 273P.46 1.33. a) true b) false c) false d) false 5. a) There is a student who spends more than 5 hours every weekd
10、ay in class.b) Every student spends more than 5 hours every weekday in class. c) There is a student who does not spend more than 5 hours every weekday in class.d) No student spends more than 5 hours every weekday in class. 9. a) x(P(x)Q(x)b) x(P(x)Q(x)c) x(P(x)Q(x)d) x(P(x)Q(x)16. a) true b) false c
11、) true d) false24. Let C(x) be the propositional function “x is in your class.” a) x P(x) and x(C(x) P(x), where P(x) is “x has a cellular phone.”b) x F(x) and x(C(x)F(x), where F(x) is “x has seen a foreign movie.”c) x S(x) and x(C(x)S(x), where S(x) is “x can swim.”d) x E(x) and x(C(x) E(x), where
12、 E(x) is “x can solve quadratic equations.”e) x R(x) and x(C(x)R(x), where R(x) is “x wants to be rich.”62. a) x (P(x)S(x) b) x(R(x)S(x) c) x (Q(x)P(x) d) x(Q(x)R(x)e) Yes. If x is one of my poultry, then he is a duck (by part(c), hence not willing to waltz (part (a). Since officers are always willi
13、ng to waltz (part (b), x is not an officer.P.591.412. d) x C(x, Bob)h) x y (I(x) (x y) I(y)k) x y( I(x) C(x, y)n) x y z (x y) (C(x, z) C(y, z)14.a) x H(x), where H(x) is “x can speak Hindi” and the universe of the discourse consists of all students in this class.b) x y P(x, y), where P(x, y) is “x plays y.” and the universe of the di
