Let D(p,d) = \"Person p owns bird d.\" Express the following in predicate form;

Question

Let D(p,d) = "Person p owns bird d." Express the following in predicate form; e.g.. ApEd D(p,d) (use A for "for all" and E for "there exists" )

A. There is a bird that belongs to everyone.

B. Everyone has a bird.

C. There is a person who owns all birds.

D. Every bird has an owner.

E. The statement "There is a bird with no owner" is false.

HINT: Your answer must start with a - sign. First, write the statement in the quotes, then negate it. Do not use any parens, except in D(p,d).

F. No one has a bird.

Explanation / Answer

A. The predicate of the statement "There is a bird that belongs to everyone" is:     EdAp D(p,d)

B. The predicate of the statement "Everyone has a bird" is:     ApEd D(p,d)

C. The predicate of the statement "There is a person who owns all birds" is:     EpAd D(p,d)

D. The predicate of the statement "Every bird has an owner" is:     AdEp D(p,d)

E. The predicate of the statement "The statement "There is a bird with no owner" is false" is:     ~"Ed~Ep D(p,d)"

The predicate of the given statement starts with a negation sign since the statement in quotes need to be false. Also, "there is no owner for bird d" is equivalent to saying that "there is a person p who owns bird d is false" which is denoted by "~Ep D(p,d)".

F. The statement "No one has a bird" is negation of the statement "Everyone has a bird" used in Part B, therefore its predicate is:     ~"ApEd D(p,d)"

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