Answer to Question #322748 in Discrete Mathematics for john xina

Question

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.

a) Someone in your class can speak Hindi.

b) Everyone in your class is friendly.

c) There is a person in your class who was not born in California.

d) A student in your class has been in a movie.

e) No student in your class has taken a course in logic programming.

Answer 1

$Q\left( x \right) =\left\{ x\,\,in\,\,class \right\} \\a:\\P\left( x \right) =\left\{ x\,\,speaks\,\,Hindi \right\} \\Domain=class:\exists xP\left( x \right) \\Domain=people:\exists x\left( Q\left( x \right) \land P\left( x \right) \right) \\b:\\P\left( x \right) =\left\{ x\,\,is\,\,friendly \right\} \\Domain=class:\forall xP\left( x \right) \\Domain=people:\forall x\left( Q\left( x \right) \rightarrow P\left( x \right) \right) \\c:\\P\left( x \right) =\left\{ x\,\,was\,\,born\,\,in\,\,California \right\} \\Domain=class:\exists x\lnot P\left( x \right) \\Domain=people:\exists x\left( Q\left( x \right) \land \lnot P\left( x \right) \right) \\d:\\P\left( x \right) =\left\{ x\,\,has\,\,been\,\,in\,\,a\,\,movie \right\} \\Domain=class:\exists xP\left( x \right) \\Domain=people:\exists x\left( Q\left( x \right) \land P\left( x \right) \right) \\e:\\P\left( x \right) =\left\{ x\,\,has\,\,taken\,\,a\,\,course\,\,in\,\,\log ic\,\,program\min g \right\} \\Domain=class:\forall x\lnot P\left( x \right) \\Domain=people:\forall x\left( Q\left( x \right) \rightarrow \lnot P\left( x \right) \right)$