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Answers to Odd-Numbered Exercises CHAPTER 1 Section 1.1 t. a) Yes, Tb) Yes, Fc} Yes, Td) Yes, Fe) No f)No 3.a) Today is not Thursday.) There is pollution in New Jersey. c)2+143. d) The summer in Maine is not hot or it is not sunny. 5. a) Sharks have not been spotted near the shore. b) Swimming at the New Jersey shore is allowed, and sharks have been spotted near the shore. c) Swimming at the New Jersey shore is not allowed, or sharks have been spotted near the shore. d) If swimming at the New Jersey shore is allowed, then sharks have not been spotted near the shore. _e) If sharks have not been spotted near the shore, then swimming at the New Jersey shore is allowed. ) If swimming at the New Jersey shore is not allowed, then sharks have not been spotted near the shore. g) Swimming at the New Jersey shore is allowed if and only if sharks have not been spotted near the shore. _h) Swimming at the New Jersey shore is not allowed, and either swimming at the New Jersey shore is allowed or sharks have not been spotted near the shore. (Note that we were able to incorpo- rate the parentheses by using the word “either” in the second half of the sentence.) 7.a)p Ag b)pA-q e)-pA-—gqg NDpvq dp>g H(pvgyA(po-4a) haope 9.a) mp b) pA-@ po adap -¢ yp>q DNar7p arp h.a)r aap byapAgar r+ @enp) a} agarpar eg Sr Aap) Ar Amp) > 9) Dar) -¢ 13, a)False b)True ¢)True d)True 15.a) Exclu- sive or: You get only one beverage. b) Inclusive or: Long passwords can have any combination of symbols. ¢) Inclu- sive or: A student with both courses is even more qualified, d) Either interpretation possible; a traveler might wish to pay with a mixture of the two currencies, or the store may not allow that. 17. a) Inclusive or: It is allowable to take discrete mathematics if you have had calculus or computer science, or both, Exclusive or: It is allowable to take discrete mathematics if you have had calculus or computer science, but not if you have had both, Most likely the inclusive or is intended. b) Inclusive oz: You can take the rebate, or you can get a low-interest loan, or you can get both the rebate and a low-interest loan. Exclusive or: You can take the rebate, or you can get a low-interest loan, but you cannot get beth the rebate and a low-interest loan. Most likely the exclusive or is intended. ¢) Inclusive or: You can order two items from column A and none from column B, or three items from column B and none from column A, or five items including two from column A and three from column B. Exclusive or: ‘You can order two itemsfrom column A or three items from column B, but not both, Almost certainly the exclusive or is intended. d) Inclusive or: More than 2 feet of snow or windchill below ~100, or both, will close school. Exclusive or: More than 2 feet of snow or windchill below — 100, but not both, will close school. Certainly the inclusive or is intended. 19, a) If the wind blows from the northeast, then it snows. b) If it stays warm for a week, then the apple trees will bloom. ¢) If the Pistons win the championship, then they beat the Lakers. d) If you get to the top of Long’s Peak, then you must have walked 8 miles. e) [f you are world-famous, then you will get tenure as a professor. f) If you drive more than 400 miles, then you will need to buy gasoline. g) If your guarantee is good, then you must have bought your CD player less than 90 days ago. _h) If the water is not too cold, then Jan will go swimming. 21. a) You buy an ice cream cone if and only if it is hot outside. b} You win the contest if and only if you hold the only winning ticket.) You get promoted if and only if you have connections. d) Your mind will decay if and only if you watch television. e) The train runs late if and only if it is a day I take the train. 23. a) Converse: “] will ski tomorrow only if it snows today.” Contrapositive: “Tf I do not ski tomorrow, then it will not have snowed to- day.” Inverse: “Tf it does not snow today, then I will not ski tomorrow.” _b) Converse: “If I come to class, then there will be a quiz.” Contrapositive: “If 1 do not come to class, then there will not be a quiz.” Inverse: “If there is not going to be a quiz, then 1 don’t come to class.” ¢) Converse: “A positive integer is a prime if it has no divisors other than | and itself.” Contrapositive: “If a positive integer has a divisor other than | and itself, then it is not prime.” Inverse: “Ifa positive integer is not ptime, then it has a divisor other than | and itself.” 25. a)2 b) 16 0) 64d) 16 27. a) p [| ap | pAnp b}p [ap | PAP TT? F TTF t F| Tt E FLT T Dp _4|-9|ev-9g[@v-)—4 T T/F] T T trelt] or F FT| EF F T F Fi] T| T F Dp gi pvalpag{@va-ern TT) tT | T T tTrFi/ tT | F F FT] tT] F F FF] F | F T 
