Reasoning: An Introduction to Logic, Sets, and Functions

Two key differences between predicate logic and Boolean logic are:

In Boolean logic, our building blocks were complete logical statements. For example, we gave the name W to the claim, “The sidewalks are wet.” In predicate logic, we’ll start with objects, like Smokey, and then build up our claims about them.
In Boolean logic there was no way to generalize and make a single claim about many different objects (except by explicitly conjoining statements about each of them as individuals). In predicate logic, the quantifiers ∀ and ∃ will let us make such general claims in a single statement.

Now we’re ready to start with the building blocks of predicate logic. We’ll use:

drawn from our universe of discourse.
that may take on as their values any of the objects that we can talk about.
that apply to objects and return objects.
, which are a special kind of function. A predicate must return a Boolean value (i.e., T or F). The job of objects and functions is to provide fodder to predicates. Predicates enable us to build logical expressions that we can reason with.

1. Consider the wff:

Complete each of these statements:

Meat is a(n): object

Sausage is a(n): object