Answer to Question #328787 in Discrete Mathematics for hesham

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

(a) Let P(x) - ''x is in your class", Q(x) - " x has a cellular phone"

1. When the domain consists of the students in your class

$\forall x: Q(x)$

2. When the domain consists of all people

$\forall x:P(x)\to Q(x)$

(b) Let P(x) - ''x is in your class", Q(x) - " x seen a foreign movie"

1. When the domain consists of the students in your class

$\exists x:Q(x)$

2. When the domain consists of all people

$\exist x:P(x)\to Q(x)$

(c) Let P(x) - ''x is in your class", Q(x) - " x cannot swim"

1. When the domain consists of the students in your class

$\exists x:Q(x)$

2. When the domain consists of all people

$\exist x:P(x)\to Q(x)$

(d) Let P(x) - ''x is in your class", Q(x) - " x can solve the quadratic equations"

1. When the domain consists of the students in your class

$\forall x: Q(x)$

2. When the domain consists of all people

$\forall x:P(x)\to Q(x)$

(e) Let P(x) - ''x is in your class", Q(x) - " x does not want to be rich"

1. When the domain consists of the students in your class

$\exists x:Q(x)$

2. When the domain consists of all people

$\exist x:P(x)\to Q(x)$