Question

Let C(x) be the statement student 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 each of these statements in terms of C(x), D(x), F(x), quantifiers, and logical connectives and then negate each of them. Let the domain consist of all students in your class, call it D.

(a) A student in your class has a cat, a dog, and a ferret.

(b) All students in your class have a cat, a dog, or a ferret.

(c) Some student in your class has a cat and a ferret, but not a dog.

Just want to check my negations

Answer 1

(a)

A student in your class has a cat,a dog and a ferret.

Negation :

So,

Every student in your class has not a cat nor a dog nor a ferret.

(b)

All students in your class have a cat, a dog , or a ferret

Negation :

So,

Some students in your class have neither a cat nor a dog nor a ferret.

(c)

Some student in your class has a cat and a ferret but not a dog

Negation

So

All students in your class has not a cat nor a dog or have a ferret.