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Discrete Math HW 2 - HW#2 CE 2305 Exercise 1.3 7 a All the...

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HW#2 CE 2305 Exercise 1.3 7) a) All the comedians are funny. b) All people are comedians and funny. c) There exists one person if he/she is comedian then he/she is funny. d) There exists one person who is comedian and is funny. 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)) 25) Let P(x) = x is perfect and Q(x) = x is your friend and the domain be all the people. a) x¬P(x) b) ¬ x P(x) c) x (Q(x)→P(x)) d) x(Q(x) P(x)) e) xQ(x) xP(x) f) (¬ x Q(x)) ( x¬P(x)) 37) a) Let P(x) = x qualifies as an elite flyer, Q(x) = x flies more than 25000 miles and R(x) = x takes more than 25 flights during that year. x [(Q(x) R(x)) → P(x)]
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HW#2 CE 2305 b) Let A(x) = x is a man, B(x) = x is a woman, C(x) = x qualifies for the marathon, P(x) = x best time is less than 3 hours and Q(x) = x best time is less than 3.5 hours. x[[(A(x) P(x)) → C(x)] [(B(x) Q(x)) → C(x)]] c) Let A(x) = x must take at least 60 course hours, B(x) = x must take at least 45 course hours and write a master’s thesis, C(x) = x must receive a grade no lower than a B in all required courses, D(x) = x will receive a master degree. x[[[A(x) B(x)] C(x)] →D(x)] d) Let A(x) = x has taken more than 21 credit hours in a semester, B(x) = x received all A’s. x[A(x) B(x)] 41) a) Let P(x,y) = Disk x has more than y kilobytes of free space, Q(x) = Mail message x can be saved. xP(x,10)→ xQ(x) b) LetA(x) = Alert x is active, B(x) = Message x is queued and C(x) = Message x is transmitted. [ xA(x)]→ x[B(x)→C(x)] c) Let P(x) = Diagnostic monitor tracks the status of system x and Q(x) = Status of the main console.
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