HW03 - CSE260 Solutions to Homework Set#3 23 Translate in...

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CSE260 Solutions to Homework Set #3 23. Translate in two ways each of these statements into logical expressions using predicates, quantifiers, and logical connectives. First, let the domain consist of the students in your class and second, let it consist of all people. Let C(x) be the propositional function “x is in your class”. a) Someone in your class can speak Hindi. 5 xH(x) and 5 x(C(x) /\ (H(x)), where H(x) is “x can speak Hindi”. b) Everyone in your class is friendly. 2200 F(x) and 2200 x(C(x) → F(x)), where F(x) is “x is friendly”. c) There is a person in your class who was not born in California. 5 x¬B(x) and 5 x(C(x) /\ ¬B(x)), where B(x) is “x was born in California”. d) A student in your class has been in a movie. 5 xM(x) and 5 x(C(x) /\ M(x)), where M(x) is “x has been in a movie”. e) No student in your class has taken a course in logic programming. 2200 x¬L(x) and 2200 x(C(x) → ¬L(x)), where L(x) is “x has taken a course in logic programming”. 41. Express each of these system specifications using predicates, quantifiers, and logical connectives. a) At least one mail message, among the nonempty set of messages, can be saved if there is a disk with more than 10 kilobytes of free space. ( 5 xF(x, 10)) → 5 xS(x), where F(x, y) is “Disk x has more than y kilobytes of free space”, and S(x) is “mail message x can be saved”.

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