Convert the following givens into formal predicate logic. Use the predicates given, you may not need all of them Then, negate the predicate sentence. Push all negations to the closest terms
a) All wooden furniture is heavy. Let the domain of discourse be all objects.
- Wooden(x): True if x is made of wood
- Furniture(x): True if x is furniture
- Heavy(x) : True if x is heavy
b) Everyone likes at least one hobby. Let the domain of discourse be all people and hobbies
- Hobby(x): True if x is a hobby
- Person(x): True if x is a person
- Likes(x,y): True if x likes y
For part a) I got:
$\forall x(Wooden(x)\land Furniture(x)\implies Heavy(x))$
And
$\exists x(\lnot Wooden(x)\lor\lnot Furniture(x) \implies Heavy(x))$
Is that correct? Also I am unsure how to start part b
The original statement in a) is correct, but the negation has been formed incorrectly. The actual negated statement should be:
$\exists x(Wooden(x)\land Furniture(x)\land\lnot Heavy(x))$
Statement b) would have the following form:
$\forall x(Person(x)\implies\exists y(Hobby(y)\land Likes(x,y)))$
And the negated statement would be:
$\exists x(Person(x)\land\forall y(Hobby(y)\implies\lnot Likes(x,y)))$