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Discrete_Assignment1_solutions - MA2201/082022 DISCRETE...

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Unformatted text preview: MA2201/082022 DISCRETE MATHEMATICS NAME: m SECTION: ASSIGNMENT 1 NAME: __._____ SECTION: PIS, 16bc, 18 bcde, 24a, 28bd, NAME: ____________ SECTION: _ ‘ 32c, 38b, 40, 44*, 480d, 56* 58*, l 64*, p.28 6, Bab, 10c, 14*, 26*, 34c. P.18 EXCLc/fiucé b) Lunch includes SOup or salad. 0) To enter the country you need a paSSport or a voter registration card. 1‘thqu V5 i i . . u - u i 16. Determine whether an Incluswe or exlcuswe or 1s Intended. } _.._.—-———-" i i i 18. Write in the form “if p, then q”. b) Winds from the south irnpl a spring thaw QJW W W — / m y ' M 4x 5L WW 0) a sufficient condition for the warranty to be good is that you bought the computer less than a year ago. (id-W W Wet’éadmma 0'! W232}; d) Willy gets caught Whenever he cheats. Mail? (5% 2 I a; 25232;» he. ‘ e) You can access the websi e only if you p a subscription fee. - & 1442M MWLM, WWW [Cr/MM!- 24. a) If it snows toni ht, then will stay at home. Converse: %} QM W Jim {7/— w‘ WW Contrapositive: Qflr/m-f‘yfl? W, m... J‘MWWW Inverse: #9; m MWZEVWW QMM %% 28. Construct a truth table: £9 F _ "" ->“1 *1 "9 fl MI, P 6-7 .19 MpHfip T g d) (29M) —+ (19W) 32. e) Construct a truth table: (p V q)/\ ——; r 38. b) Evaluate (0 1111A 10101)v 0 1000 {00I0i)v(01000)-0H0! 40. The truth value of “Fred is happy” is .8, and of “John is happy’ is .4 What is the truth value of: “Fred and John are happy” '"9WL81 3) What is the truth value of; “Neither Fred nor John is haEpy”. My M M>FAL¢£DIM -MWe—7W(.1yé) :2"; i 44. A barber shaves those people, and only thos eople, who do not shave themselves. Can there be such a barber? 5" (”I MEMMWW/ Au: LWWWM gym. ' WWW EWW CONTWCA’DbaWOA-f CAL fickw. i l 48. Given the prOpositions p “The user enters a valid password” q “Access is granted” and r “The user has paid the subscription fee.” Write the following using 3), q, 7" and logical connectives. 0) “Access is denied if the user has not paid the subscription fee.” l "V’— “7 a? (9" €79 ’1') d) “If the user has not entered a valid password but has paid the subscription fee, then access is granted.” a]? A h, ___> Knights always tell the truth and knaves always lie. ’4 W”? g/é’wa/“lm 5/4 Md: A W A says “The two of us are both knights” nd B sa 5 “ is a knave.” What are A and B? 8 km W 4.4- 6 M " ‘ 8. Both A and 13 say “I am a knight.” What are A and B? 41? E 2 - 64. Four friends are suspects. Alice said “Carlos did it.” John said “I did not do it.” Carlos said “Diana did it.” Diana said “Carols lied when he said that I did it.” a) If only one of the four is telling the truth, who did it? Explain. C b) If exactly one is lying, who did it? Explain. a7 mam mm o —m. Sélémzma ~mm,mmw ) WTWM ‘WI 6?, ‘Wa fig ' Madam MMJfirifl‘x ' “Ax—WM dag}; M, W “'3 “ mammmga/Jm M W Maia, ‘ fin—om PW) M U W fa. 71 Yoshiko knows Java and Calculus V: at! “hmwk : ,J‘ I 6’!— £’ 2 Mémmlm Use a truth table to show that [p /\ p —> q)] M, q is a tautology. "—5 E - its a M MM wane will take a job in industry or go to graduate school WW ) b) ) 10. 7 FTZM,W~ TP/leAeDm ,MW “1%me my ‘ . ' ,1 NOT at 77rdde 63 1% M )‘chw ”’19 Myaawwj WMMP/LZLMW; g,— 14. Determine whether (—7 p /\ (p re (1)) —>—7 q is a tautology (without truth table). 26. Show that '—r p —> (q —> r) and q —> (p V r) are logically equivalent (without truth table). of alarm) e—> [3 var-am) €—> PVC'fiLWZ—W lip/(Wt) 3 ‘3 0i a (r M 34 c) Find the dual of the compound proposition (p/\ w (1) V (q /\ F) (Pv'ifi/ngfl m. CPVW‘JQAT M gov-"17y ...
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