Validity of Predicate Statements Examples

In this class, We discuss the Validity of Predicate Statements Examples.

The reader should have prior knowledge of equivalence formulas. Click Here.

Example:

Given statements.

Every living thing is a plant or animal.

Joe’s Goldfish is alive, and it is not a plant.

All animals have hearts.

In conclusion, Joe’s Goldfish had a heart from the above statements.

Solution:

Converting the statements to predicate formulas is important.

Given the universe of discourse is all living things.

P(x): x is a plant

A(x): x is an Animal.

H(x): x has a heart.

f: Joe Goldfish

The statements are written as below

(x)(P(x) ∨ A(x))

¬P(f)

(x)(A(x) -> H(x))

Conclude H(f) from the above statements.

The below diagram shows the derivation.