Answer to Question #259075 in Discrete Mathematics for Afrah

Question

Use quantifiers and predicates with more than one vari-

able to express these statements.

a) There is a student in this class who can speak Hindi.

b) Every student in this class plays some sport.

c) Some student in this class has visited Alaska but has

not visited Hawaii.

d) All students in this class have learned at least one pro-

gramming language.

) There is a student in this class who has taken ev-

ery course offered by one of the departments in this

school.

1) Some student in this class grew up in the same town

as exactly one other student in this class.

Choosing the correct answer step by step

Answer 1

Student(x) - x is a student in this class, speak(x, y) - x speaks y, sport(x, y) - x plays y, visit(x, y) - x visited y, learn(x ,y) - x learned y, offered(x, y) - department x offered course y, take(x, y) - x take course y, grew(x , y) - x grew in the same town as y

a). There is a student in this class who can speak Hindi

$\exists x:(student(x)\land speak(x,Hindi))$

b) Every student in this class plays some sport

$\forall x \exists y:(student(x)\to sport(x,y))$

c) Some student in this class has visited Alaska but has not visited Hawaii

$\exist x:(student(x)\land visit(x, Alaska) \land \lnot visit(x, Hawaii))$

d) All students in this class have learned at least one programming language.

$\forall x\exists y:(student(x)\to learn(x,y))$

e) There is a student in this class who has taken every course offered by one of the departments in this

school.

$\exist x \exists z \forall y:((student(x) \land offered(z,y))\to take(x,y))$ , Y - set of courses offered by one of the school departments

1) Some student in this class grew up in the same town as exactly one other student in this class.

$\exist x \exists !y:(student(x) \land student(y)\land grew(x,y))$