# predicates and quantifier problems

• Jun 28th 2007, 05:41 PM
Discrete
predicates and quantifier problems
Let C(X0 be the statement "x has a cat", let D(x) be the statement "x has a dog" and let F(x) be the statement "x has a ferret". Express the statements in terms if the C(x),D(x), and F(x), quantifiers, and logical connectives. Let the domain be all student in class.

a. For each of the three animals, cats,dogs,and ferrets, there is a student in your class who has one of these animals as a pet.

$\displaystyle \exists x [C(x) \vee D(x) \vee F(x)]$

Express these statements without using quantifiers, instead using only negations, disjunctions, and conjunctions.

$\displaystyle \exists x(\neq P(x)) \wedge \forall x((x < 0) \rightarrow P(x))$

$\displaystyle [\neg P(-5) \vee \neg P(-3) \vee \neg P(-1) \vee \neg P(1) \vee \neg P(3) \vee \neg P(5)] \wedge [P(5) \wedge P(3) \wedge P(1)]$
• Jun 29th 2007, 06:43 AM
Plato
Quote:

Originally Posted by Discrete
Let C(X0 be the statement "x has a cat", let D(x) be the statement "x has a dog" and let F(x) be the statement "x has a ferret". Express the statements in terms if the C(x),D(x), and F(x), quantifiers, and logical connectives. Let the domain be all student in class.
a. For each of the three animals, cats,dogs,and ferrets, there is a student in your class who has one of these animals as a pet.

Note that this says that at least one in the class owns a cat, at least one in the class owns a dog, and at least one in the class owns a ferret.
$\displaystyle \left( {\exists x} \right)\left( {\exists y} \right)\left( {\exists z} \right)\left[ {D(x) \wedge C(y) \wedge F(z)} \right]$.

I have absolutely no idea what you are doing in the second part.