Answer to Question #307483 in Discrete Mathematics for amir

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) Everyone in your class has a cellular phone. b) Somebody in your class has seen a foreign movie. c) There is a person in your class who cannot swim. d) All students in your class can solve quadratic equations. e) Some student in your class does not want to be rich

Answer 1

First expression has domain consists of all your classmates, secon - of all people

a) Everyone in your class has a cellular phone. Let A(x) - x has a cellular phone. B(x) - x is your classmate

$\forall x:A(x)$

$\forall x: B(x)\implies A(x)$

b) Somebody in your class has seen a foreign movie. Let A(x) - x has seen a foreign movie. B(x) - x is your classmate

$\exists x:A(x)$

$\exists x: B(x)\implies A(x)$

c) There is a person in your class who cannot swim. Let A(x) - x cannot swim. B(x) - x is your classmate

$\exists x:A(x)$

$\exists x: B(x)\implies A(x)$

d) All students in your class can solve quadratic equations. Let A(x) - x can solve quadratic equations. B(x) - x is your classmate

$\forall x:A(x)$

$\forall x: B(x)\implies A(x)$

e) Some student in your class does not want to be rich. Let A(x) - x does not want to be rich. B(x) - x is your classmate

$\exists x:A(x)$

$\exists x: B(x)\implies A(x)$